INSCRIBING MEDIEVAL PEDAGOGY:MUSICA FICTA IN ITS TEXTS

by

CLÓVIS AFONSO DE ANDRÉMay 9th, 2005

Major Professor: Dr. Michael Long

A dissertation submitted to theFaculty of the Graduate School of

The State University of New York at Buffaloin partial fulfillment of the requirements for the

degree of

Doctor of Philosophyin

Historical Musicology

Department of Music

INSCRIBING MEDIEVAL PEDAGOGY:MUSICA FICTA IN ITS TEXTS

by

CLÓVIS AFONSO DE ANDRÉMay 9th, 2005

A dissertation submitted to theFaculty of the Graduate School of

The State University of New York at Buffaloin partial fulfillment of the requirements for the

degree of

Doctor of Philosophyin

Historical Musicology

Department of Music

Copyright by

Clóvis Afonso de André

2005

ii

To

my wife and kids

Lúcia, Lucas, and Pedro

and

my brother

Paulo de Tarso A. de André

(in memoriam)

iii

ACKNOWLEDGMENTS

First, and most significantly, I owe a great deal of gratitude to my advisor and friend,

Dr. Michael Long, without whose trust, guidance and constant encouragement this work

would never have come to completion. Even where he did not agree with some of my

interpretations, his suggestions and immense editing effort always invited more research and

a better elaboration of my thoughts, sometimes with an ability to comprehend them even in

incomplete stages of articulation—there are just no words that could thank him enough.

The other members of my committee, Dr. Martha Hyde and Dr. Peter Schmelz, were also

immensely helpful with insights and suggestions to improve on my work, and I am grateful

for the time and energy they spent in further revising my prose, as well as for the motivation

and privilege they granted me by agreeing to serve as members of my committee. Owing to

a number of practical and bureaucratic constraints, neither Dr. Long nor the other committee

members received a copy of my dissertation draft until shortly prior to the deadline for

deposit. Therefore, I duly apologize to them and to the reader for any remaining errors of

grammar and syntax, or other unidiomatic resonances of my native language of Portuguese

in the text. Also, I wish to thank for the help received from various scholars who have

generously granted me copies of their papers (even when I was living abroad, and could not

attend to their lectures), and for the opportunity of exchanging some correspondence on

iv

particular issues of the dissertation. In this respect, I would like to cite Margaret Bent,

Mariamichela Russo, Eleonora Beck, Stefano Mengozzi, Peter Urquhart, Elizabeth

Kotzakidou-Pace, and Sigrun Heinzelmann—who I hope will forgive if I do not mention

their academic titles. Other distinguished professors (and above all friends) have also

honored me with their contributions, and valuable advice within and outside their area of

expertise (from theoretical and methodological approaches to linguistic issues), in several of

the formative stages of this project: John Clough, Gary Burgess, James Patrick, Christopher

Gibbs, Rebecca Maloy, Francesca Behr, José Luiz Martinez, Fernando José Carvalhaes

Duarte, Hildebrando de André, John Spindler, and David Frew. Of invaluable aid I must

mention the librarians and staff of the UB Music Library, who helped with their friendship

and exceptional work: Nancy Nuzzo, Rick McRae, John Bewley, James Coover, and Joanne

Dudak. This work would also not have been possible without the online databases (SMI,

TFM, TME, and TML) under the general direction of Thomas Mathiesen in the Center for

the History of Music Theory and Literature at the Indiana University. These databases and

the UB Libraries online system, were of particular help when I had to move back to Brazil

(from Sept. 1999 onward), where I have very limited access to scholarly works and treatises

in general. Despite those limitations, it was also essential to count on the support of my

current employers, for which I been serving as Professor of Music History, in charge of a

three-year Survey at Faculdade Santa Marcelina (since Sept. 2000) and of a four-year

Survey at Faculdades Integradas Cantareira (since Sept. 2004), both in São Paulo. The

v

deans of these institutions granted me a three-week leave for the dissertation defense (from

late April to mid May), even though the academic semester in Brazil ends on June 30th.

Three most significant grants also allowed the completion of this dissertation: the

generous provision of a Dissertation Fellowship from the College of Arts and Sciences at

the University at Buffalo (in 2003); a travel Grant on Cultural Diversity from the American

Musicological Society (which covered my expenses during the Boston Meeting in 1998)

without which I would not have been able to attend important sessions dealing with the

subject of this dissertation; and finally, the extended and honorable Doctorate Grant

provided by the Brazilian Government through the Conselho Nacional de Desenvolvimento

Científico e Tecnológico (CNPq) from 1995 to 1999.

My warmest thanks is due to my wife, Lúcia Ramos, for her learned support,

welcome criticism, love and self-sacrifice throughout the seven or eight years from the first

conception of this project to its completion. Nothing would have been conceivable or have

any meaning without her, nor without the additional inspiration provided by the love and

laughter of our two sons. Finally, I wish to thank my mother and father, Clarisse Parisotto

and Bruno, for without their loving and caring support I would never have made through

this point in my life. My father is also responsible for many discussions and opinions

about rhetoric that were essential to my comprehension of the subject, as well as for

discussions about judicial issues regarding the Corpus iuris civilis which, I hope, will come

to fruition in a further elaboration of the present work relating musica ficta to medieval law.

vi

TABLE OF CONTENTS

DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

EDITORIAL NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

BIBLIOGRAPHICAL ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx

GENERAL ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

vii

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv

SUMMARY OF CHAPTERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxvi

CHAPTERS

CHAPTER 1 — THE GAMUT, MUSICA FICTA AND MUSICA RECTA

(i) The Gamut: A Presentation and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

(ii) Musica ficta versus Musica recta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

CHAPTER 2 — PRINCIPLES OF HEXACHORDAL SOLMIZATION

(i) Deduction of Hexachords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

(ii) Stages of Solmization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

(iii) Recognition and Reading of Hexachords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

(iv) Equivalence Between Hexachords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

(v) Refutation: Resistance to Hexachordal Solmization . . . . . . . . . . . . . . . . . . . . . 93

(vi) Working beyond the limits of the hexachord . . . . . . . . . . . . . . . . . . . . . . . . . . 107

CHAPTER 3 — MUTATION: THE BASICS

(i) Mutation (basic concepts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

(ii) Mutation (basic cases, processes and guidelines) . . . . . . . . . . . . . . . . . . . . . . . 133

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CHAPTER 4 — MUTATION: IRREGULAR TYPE, FICTA-SPECIES, AND

POSITION OF FICTA-SIGNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

CHAPTER 5 — PERMUTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

CHAPTER 6 — TRANSMUTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

CHAPTER 7 — FIGURES OF SOLMIZATION AND FIGURES OF

RHETORIC: THE MUSICAL DISCOURSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

CHAPTER 8 — ISSUES OF TERMINOLOGY: FORGING TERMS,

DEFINITIONS, AND CONCEPTS IN MODERN SCHOLARSHIP

(i) Generic Definitions: The Audience Considered . . . . . . . . . . . . . . . . . . . . . . . . 273

(ii) Particular Terminology: Accidentals Versus Ficta-signs . . . . . . . . . . . . . . . . . 296

(iii) Particular Terminology: Other Terms Versus Ficta-signs . . . . . . . . . . . . . . . . 311

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

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LIST OF FIGURES

CHAPTER 1

FIGURE 1 .1 – Recta-Gamut (post-Guido d'Arezzo) . . . . . . . . . . . . . . . . . . . . . . . . . 2

FIGURE 1 .2 – "Ut queant laxis" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

FIGURE 1 .3 – "Trinum et unum" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

FIGURE 1 .4 – "Domine qui operati sunt" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

FIGURE 1 .5 – "Alliga Domine in vinculis" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

FIGURE 1 .6 – "Beatus servus" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

CHAPTER 2

FIGURE 2 .1 – "Puer natus" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

FIGURE 2 .2 – "Omnes de saba" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

FIGURE 2 .3 – Recognition of hexachords (fifth-span, no explicit semitone) . . . . . 64

FIGURE 2 .4 – "Ut queant laxis"—solmization of -hexachord . . . . . . . . . . . . . . . 67

FIGURE 2 .5 – Recognition of hexachords (fifth-span, no explicit semitone) . . . . . 74

FIGURE 2 .6 – Octave equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

FIGURE 2 .7 – "Accueily m'a belle" (contratenor), by Phillippe Caron . . . . . . . . . . 77

FIGURE 2 .8 – "Kyrie eleison," from Mass XI "Orbis factor" . . . . . . . . . . . . . . . . . . 78

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FIGURE 2 .9 – "Ave Regina caelorum" (contratenor)—(Gallicus 1458/64) . . . . . . . . 79

FIGURE 2.10 – "Ave Regina caelorum" (contratenor)—(Gallicus 1458/64) . . . . . . . 81

CHAPTER 3

FIGURE 3 .1 – Mutation (from - to -hexachord) . . . . . . . . . . . . . . . . . . . . . . . . . 143

FIGURE 3 .2 – Mutation (from - to -hexachord) . . . . . . . . . . . . . . . . . . . . . . . . . 143

FIGURE 3 .3 – Mutation (from - to -hexachord, forced by ficta-sign) . . . . . . . . . 147

FIGURE 3 .4 – Mutation (from - to - to -hexachord, forced by ficta-sign) . . . . 148

FIGURE 3 .5 – Mutation (various)—(Guerson [ca. 1495]) [original notation] . . . . . 150

FIGURE 3 .6 – Mutations (various)—(Guerson [ca. 1495]) [transcription] . . . . . . . 152

FIGURE 3 .7 – 'Indirect' mutation on rest—"Garrit gallus" (mm. 54–60) . . . . . . . . 158

FIGURE 3 .8 – 'Indirect' mutation on note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

CHAPTER 4

FIGURE 4 .1 – Recta- and Ficta-mutation—"Navré je sui" (refrain), by Du Fay . . . 169

FIGURE 4 .2 – Ficta-mutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

FIGURE 4 .3 – Functions of ficta-signs—(Ornithoparchus 1517) [original notation] 174

FIGURE 4 .4 – Functions of ficta-signs—(Dowland 1609), revised version of

Ornithoparchus's example [original notation] . . . . . . . . . . . . . . . . . 175

FIGURE 4 .5 – Functions of ficta-signs—Dowland's revised version of

Ornithoparchus's example [transcription] . . . . . . . . . . . . . . . . . . . . 176

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FIGURE 4 .6 – Functions of ficta-signs (ficta-mutation) . . . . . . . . . . . . . . . . . . . . . 178

FIGURE 4 .7 – Functions of ficta-signs (ficta-mutation) . . . . . . . . . . . . . . . . . . . . . 179

FIGURE 4 .8 – Functions of ficta-signs (ficta-mutation) . . . . . . . . . . . . . . . . . . . . . 181

CHAPTER 5

FIGURE 5 .1 – Stepwise permutation—(Marchettus da Padova 1317/18) . . . . . . . . 193

FIGURE 5 .2 – Stepwise permutation—"Garrit gallus" (mm. 54–60) . . . . . . . . . . . 196

FIGURE 5 .3 – Permutation by leap—(Gaffurius 1496), first solution . . . . . . . . . . . 199

FIGURE 5 .4 – Permutation by leap—(Gaffurius 1496), alternative solution . . . . . . 203

FIGURE 5 .5 – Permutation by leap of fifth (fa/fa)—(Ramos de Pareja 1482) . . . . . 213

FIGURE 5 .6 – Permutation by leap of fifth (mi/mi)—(Ramos de Pareja 1482) . . . . 215

FIGURE 5 .7 – Alternative mutations on leap of fifth (re la re and ut sol ut)—

(Ramos de Pareja 1482) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

FIGURE 5 .8 – Permutation by leap of tritone (fa/mi)—(Ramos de Pareja 1482) . . 218

FIGURE 5 .9 – Mutations on leap of sixth (mi la ut and re la ut)—

(Ramos de Pareja 1482) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

CHAPTER 6

FIGURE 6 .1 – Transmutation in fa-super-la situation . . . . . . . . . . . . . . . . . . . . . . . 223

FIGURE 6 .2 – 'Propinquity'—(Marchettus da Padova 1317/1318, tr. 5, ch. 6)

[original notation] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

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FIGURE 6 .3 – Transmutation in cadential situations ('propinquity')—(Marchettus

da Padova 1317/1318, tr. 5, ch. 6) [transcription] . . . . . . . . . . . . . . . 226

FIGURE 6 .4 – Transmutation in fa-super-la (upper-semitone) and cadential

(subsemitone) situations—melodic context . . . . . . . . . . . . . . . . . . . 229

FIGURE 6 .5 – Transmutation in fa-super-la (upper-semitone) and transitional

(diatonic and chromatic) situations—melodic context . . . . . . . . . . . 230

FIGURE 6 .6 – Transmutation in fa-super-la (upper-semitone) and other procedures

in transitional (diatonic and chromatic) situations—melodic context 231

FIGURE 6 .7 – "Ave Regina caelorum" (monophonic)—(Gallicus 1458/64) . . . . . . 240

FIGURE 6 .8 – "Ave Regina caelorum" (polyphonic)—(Gallicus 1458/64) . . . . . . . 243

CHAPTER 8

FIGURE 8 .1 – Overuse and underuse of signs ('accidentals' vs. 'ficta-signs') . . . . . 299

FIGURE 8 .2 – Absence of signs ('accidentals' versus 'ficta-signs') . . . . . . . . . . . . . 300

LIST OF TABLES

TABLE I – Gallicus's solmization for the entire gamut . . . . . . . . . . . . . . . . . . . . 104

TABLE II – The expanded (12-step) gamut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

TABLE III – Added mi-signs in Gallicus's two-voice "Ave Regina caelorum" . . . 250

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ABSTRACT

This dissertation focuses on the medieval and Renaissance understandings of

musica ficta with respect to considering its repertorial and theoretical contexts, from the

ninth to the sixteenth century. Contrary to common understandings that musica ficta was

linked primarily to the rules of counterpoint, and therefore to polyphony, the author argues

that musica ficta was the product of earlier monophonic contexts that called for solutions

mainly through solmization.

The entire process of solmization is laid out, first regarding recta solmization and

then moving to ficta solmization. The three main procedures for clarifying hexachords

(mutation, permutation, and transmutation) are discussed. Each is addressed in detail; types

and subtypes (such as 'explicit,' 'implicit,' and 'indirect' mutations), species (recta- and

ficta-mutations), cases ('regular' and 'irregular' mutations, permutations by leap and stepwise,

transmutations in upper- and subsemitone situations, as well as in propinquity) are

identified and defined. The dissertation introduces to ficta scholarship notions of

transmutation and of solmization by means of octave equivalence. In the latter, a momentary

shift between two hexachords of the same kind (say, two -hexachords in different octaves)

may be solmized without an actual change between them (i.e., without mutation).

'Transmutation' is conceived as an umbrella term that encompasses other types short-range

xiv

shifts between hexachords, in which one borrows a note from a different hexachord in order

to permit the solmization of a transitional step that falls outside of its limits. This may

happen, for example, when a note from an -hexachord is solmized within a -hexachordal

gesture, in order to momentarily reach a b above a. These concepts and terminology as

promulgated in the language of medieval didactic writings are also considered in terms of

contemporaneous rhetorical and philosophical practices, in an attempt to tease out the

conceptual background that may have informed the approaches to solmization and the

realization of musica ficta taken by theorists, pedagogues, and performers.

xv

EDITORIAL NOTES

— Double-quotes and single-quotes — Double-quotes have been used for direct

quotations, and single-quotes for emphasis on terms (musical, philosophical, rhetorical),

usually not quoted from any particular source. This procedures seeks to solve

misapprehensions of those emphasis as quoted words or short sentences. Double-quotes

have also been used for titles, incipits, or quotations of literary texts set to music—e.g.,

"Hymn to St. John" (as generic title), or "ut queant laxis" (either as incipit or as title).

— Dates of historical treatises — Two signs have been used in dates that involve

more than one single year: a dash, or a slash. A dash indicates the span of years in which

the treatise was written and/or rewritten. For instance, Pietro Aaron's Toscanello receives

the date "1523-29." In this specific case, Aaron's treatise first appeared in 1523, but was

revised and received a supplement (Aggiunta) published in 1529. A slash indicates that a

treatise was written on some date between the given span of years (i.e., the exact date is

uncertain, although the span of years in which it was written can be determined). For

instance, Johannes Gallicus's Ritus canendi receives the date "1458/64," for the exact dates

of its completion or inception are not known, although it happened some time between those

years. A letter (uppercase or lowercase) after a date indicates that an author has

xvi

produced, in the same date, two or more works. If the chronological order for those works

is known, then a lowercase letter (following alphabetical order) will be used. If the

chronological order for those works is not known, then an uppercase letter will be used

(usually taken from the first word of the title). In the bibliographical entries, the date

appears immediately before a list of sources used for consultation, which is appended to

each entry, primarily for treatises that originally circulated in manuscript form.

xvii

SYMBOLS(QUICK REFERENCE LIST)

Musical symbols

— Pitches and steps —

thru . . . . . . . . . . . . pitch-classes

a thru g . . . . . . . . . . . . pitches (boldface)— may use uppercase,lowercase, or prime-signs as needed according tomodern nomenclature

a thru g . . . . . . . . . . . . step-letters (regular typeface) — may useuppercase,lowercase, or letter doubling as neededaccording to medieval nomenclature

— Ficta-signs —

. . . . . . . . . . . . . . . . . fa-sign; or b-rotundum, b-molle

. . . . . . . . . . . . . . . . mi-sign; or b-quadratum (or quadrum), b-durum

. . . . . . . . . . . . . . . . mi-sign

— Accidentals —

. . . . . . . . . . . . . . . . flat-sign

. . . . . . . . . . . . . . . . natural-sign

. . . . . . . . . . . . . . . . sharp-sign

xviii

— Solmization —

syllable . . . . . . . . . . . Always given in italics, above the staff. In most casesthe solmization is mine. If original to a source, anappropriate reference is given in the text or in thecaption of the correspondent illustration.

= . . . . . . . . . . . . Equals sign is used in mutations.

[ ] . . . . . . . . . . . . Brackets are used in 'implicit' mutations, enclosingthe syllable that is not uttered. For example, [sol=]=re indicates that sol is being abandoned and is notuttered, while re is now uttered in its place, and is thevalid syllable for a given note.

/ . . . . . . . . . . . Slashes indicate 'permutation.' For example: fa/ /mi,where fa is the last syllable of a hexachord beingabandoned, and mi is the first syllable of thehexachord being assumed.

( ) . . . . . . . . . . . Parentheses indicate 'transmutation.'

These signs are used in the following fashion:

[syllable=] . . . . . . . . . implicit mutated syllable (non-uttered)

[=syllable] . . . . . . . . . implicit mutant syllable (non-uttered)

syllable= . . . . . . . . . . mutated syllable (uttered)—in explicit or implicit mutations

=syllable . . . . . . . . . . mutant syllable (uttered)—in explicit or implicit mutations

syllable/ . . . . . . . . . . . permutated syllable

/syllable . . . . . . . . . . . permutant syllable

(syllable) . . . . . . . . . . transmutant syllable

syllable . . . . . . . . . . . syllable solmized through octave equivalence

xix

BIBLIOGRAPHICAL ABBREVIATIONS

AM . . . . . . . . . . . . . . . Antiphonale monasticum pro diurnis horis. 1934.

Anon. ad Herennium . . . . . . Anonymous. Rhetorica ad Herennium. No dates aregiven in citations of this work.

Anon. Alia mus. ca. 890 . . . . . Anonymous. Alia musica. ca. 890.

Anon. Berkeley 1375 . . . . . . Anonymous. The Berkeley Manuscript. 1375.

Anon. Carthus. ca. 1400 . . . . Anonymous monachus Carthusiensis. Tractatus demusica plana. ca. 1400.

Anon. Cist. ca. 1147 . . . . . . Anonymous. Tractatus Cantum quem Cisterciensisordinis ecclesiae cantare consueverant. ca.1147.

Anon. 11 ?med. 15th cent. . . . . Anonymous 11. Tractatus de musica plana etmensurabili. ?med. 15th century.

Anon. Libellus 14th cent. . . . . Anonymous. [Libellus musicae] ex codice I-Rvat lat.5129. 14th century.

Anon. ME a. 900 . . . . . . . . Anonymous. Musica enchiriadis. a. 900.

Anon. SE a. 900 . . . . . . . . . Anonymous. Scolica enchiriadis. a. 900.

Anon. St Emmeram ca. 1279 . . Anonymous St Emmeram. De expositione musicae. ca.1279.

Anon. 2 ?ex. 13th cent. . . . . . Anonymous 2. Tractatus de discantu. ?ex. 13thcentury.

xx

Aristotle. Abbrev. Title . . . . . Aristotle works are given with his name and anabbreviation of title (e.g., Rhet. for Rhetorica,Top. for Topica, Meteor. for Meteorologica, etc.).No dates are given in citations of his works.

CH . . . . . . . . . . . . . . . Coussemaker, Charles-Edmond-Henri de, ed. Histoirede l'harmonie au moyen âge. 1852.

CS . . . . . . . . . . . . . . . . Coussemaker, E. de, ed. Scriptorum de musica mediiaevi, 4 vols. 1864–76.

GS . . . . . . . . . . . . . . . . Gerbert, Martin, ed. Scriptores Ecclesiastici de musicasacra potissimum., 3 vols. 1784.

HmT . . . . . . . . . . . . . . Eggebrecht, Hans Heinrich, ed. Handwörterbuch dermusikalischen Terminologie. 1972– .

LmL . . . . . . . . . . . . . . . Bernhard, Michael. Lexicon Musicum Latinum MediiAEvi. 6 vols. (each one with different date).

LU . . . . . . . . . . . . . . . . The Liber usualis. 1934.

MGG 2 . . . . . . . . . . . . . Finscher, Ludwig, ed. Die Musik in Geschichte undGegenwart. 2nd. ed. 1994–1998.

NHarvard 1986 . . . . . . . . . Randel, Don Michael, ed. The New Harvard Dictionaryof Music. 1986.

OLD . . . . . . . . . . . . . . Glare, P.G.W. Oxford Latin Dictionary. 1982.

PL . . . . . . . . . . . . . . . . Migne, Jacques-Paul, ed. Patrologiae cursus completus,series latina, 221 vols. 1844–84.

SMI . . . . . . . . . . . . . . . Giger, Andreas, dir. Saggi musicali italiani. http://www.music.indiana.edu/smi. 1997– .

SR 1950 . . . . . . . . . . . . . Strunk, Oliver, ed. and trans. Source Readings in MusicHistory. 1950.

SR 1998 . . . . . . . . . . . . . Treitler, Leo, ed. Strunk's Source Readings in MusicHistory. Revised edition. New York andLondon: W.W. Norton and Company, 1998.

xxi

TGL . . . . . . . . . . . . . . . Estienne, Henri [Henrico Stephano]. Thesaurus graecaelinguae, 9 vols. 1954.

TFM . . . . . . . . . . . . . . Slemon, Peter J., dir. Traité français sur la musique.http://www.music.indiana.edu/tfm. 2002– .

TME . . . . . . . . . . . . . . Lefferts, Peter M., dir. Texts on Music in English.http://www.music.indiana.edu/tme. 2002– .

TML . . . . . . . . . . . . . . Mathiesen, Thomas, dir. Thesaurus musicarumlatinarum. http://www.music.indiana.edu/tml.1990– .

NG 1 . . . . . . . . . . . . . . Sadie, Stanley, ed. The New Grove Dictionary of Musicand Musicians, 20 vols. 1st. ed. 1980.

NG 2 . . . . . . . . . . . . . . Sadie, Stanley, and John Tyrrell, eds. The New GroveDictionary of Music and Musicians, 29 vols.2nd. ed. 2001.

NG 2e . . . . . . . . . . . . . . Macy, Laura, ed. The New Grove Dictionary of MusicOnline. 2001– .

TLL . . . . . . . . . . . . . . . Thesaurus linguae latinae. 1900– .

Webster's 3e . . . . . . . . . . Webster's Third New International Dictionary,Unabridged. 1996– . Online version.

Webster's RH 1995 . . . . . . . Random House Webster's College Dictionary. 1995.

xxii

GENERAL ABBREVIATIONS

a. . . . . . . . . . . . . . . . . ante, beforeabl. . . . . . . . . . . . . . . . ablative (declension)acc. . . . . . . . . . . . . . . . accusative (declension)bk. . . . . . . . . . . . . . . . . book, Liber (followed by an arabic numeral—referring

to a book of a treatise, according to the divisionpresented in the sources; plural: bks.) *

ca. . . . . . . . . . . . . . . . . circa, around, about, approximatelycent. . . . . . . . . . . . . . . century (used mainly in author-date citations)ch. . . . . . . . . . . . . . . chapter, caput, capitulum (followed by an arabic

numeral—according to the division presented in thesources; plural: chs.) *

dat. . . . . . . . . . . . . . . . dative (declension)ex. . . . . . . . . . . . . . . exeunt, end of, latef. . . . . . . . . . . . . . . . . folio (plural: ff.)ff. . . . . . . . . . . . . . . . . 'and following '(this meaning is used when it is placed

after numbers of a page, folio or chapter—e.g., f.A ir ff., means, 'folio A ir and following'—thisabbreviation must not be confused with the plural'folios',which is also indicated by ff., but is placedbefore numbers)

i. . . . . . . . . . . . . . . . . inter, betweenin. . . . . . . . . . . . . . . . . ineunte, beginning of, earlyind. . . . . . . . . . . . . . . . indicative (verb tense)lit. . . . . . . . . . . . . . . . . literallymed. . . . . . . . . . . . . . . medio, midp. . . . . . . . . . . . . . . . . pagina, page (plural: pp.); post, after (this latter meaning

is used exclusively for dates of historicaltreatises)

p.a. . . . . . . . . . . . . . . . paulo ante, a little beforepl. . . . . . . . . . . . . . . . . pluralp.p. . . . . . . . . . . . . . . . paulo post, a little afterpres. . . . . . . . . . . . . . . present (verb tense)

xxiii

Ps.- . . . . . . . . . . . . . . . Pseudo- (prefix abbreviation used in citations)pt. . . . . . . . . . . . . . . . . pars, part (followed by an arabic numeral—referring to a

part of a book and/or treatise, according to thedivision presented in the sources; plural: pts.) *

r. . . . . . . . . . . . . . . . . reignedsing. . . . . . . . . . . . . . . singulars.l. . . . . . . . . . . . . . . sine loco, without places/n . . . . . . . . . . . . . . . . sine numero, without numbersubj. . . . . . . . . . . . . . . subjunctive (verb tense)s.v. . . . . . . . . . . . . . . . sub verbo, sub voce ; meaning 'under the entry' (plural:

s.vv.)tr. . . . . . . . . . . . . . . . . treatise, tractatus (followed by an arabic

numeral—referring to a part of a larger work,according to the division presented in the sources;plural: trs.) *

xxiv

INTRODUCTION

This dissertation considers musica ficta in its repertorial and theoretical contexts,

from the ninth to the sixteenth century. My purpose is, first, to present alternative

guidelines for analyzing, reading, and transcribing medieval and Renaissance compositions

with respect to musica ficta, and, second, to identify and provide an interpretation for

'rhetorical' imagery and concepts within a number of theoretical texts dealing with

solmization and with musica ficta.1 Since most of the historical texts presented ficta in

practical terms rather than speculative ones, musical and theoretical references are analyzed

primarily from the standpoint of the performer. The first part of the dissertation emphasizes

solmization (concepts, variables, and procedures) both as a determinant of and as a means

through which musica ficta is implemented, while ficta-signs are presented as indicators for

hexachordal solmization. Connections between the procedures and terminology on one

side, and rhetoric and philosophy on the other, are also introduced within those discussions.

These serve as anticipations of chapters seven and eight, which are more exclusively

dedicated to tracing those connections. My interpretations of and solutions for musica ficta,

1 The term solmization, from the Latin word solmisatio , is here used specifically for

music-reading practices, usually via a set of syllables, based on any structure smaller than octave—e.g.,

hexachordal structures. Therefore, for the sake of proper differentiation, solmization is here opposed to

solfège—a term reserved only for octave-based structures that led to modern music-reading.

xxv

involving its presentation and associated terminology in historical treatises, also reflect the

opposition between musica speculativa and musica practica, generally expressed in the

opposing definitions of musicus versus cantor—as can be attested in the following words

by Margaret Bent.

The application of musica ficta was considered part of the performer's art; this is why the

terminology of singing teaching rather than that of speculative theory is used for most

contemporary statements on the subject: some references also occur in vernacular writings of a

non-technical nature.

(NG 1, 12: 803)

Solmization, as the primary technical tool used by performers for reading and

deciphering the pitch content of an individual voice, is similarly considered from a generally

practical perspective. This concept has already been explored in noteworthy works by

Henderson (1969), Gaston Allaire (1972), Andrew Hughes (1972), Toft (1992), and in

pivotal articles by Edward Lowinsky (1945, 1956), Margaret Bent (1972, 1984, 1996),

Daniel Leech-Wilkinson (1984), Zager (1989), and others. Most scholars (as illustrated in

Margaret Bent's assessment quoted above) admit that the bulk of theoretical discourse on

musica ficta owes more to musica practica understandings than to speculativa

argumentation. Paradoxically, most have either devalued, neglected, or dismissed

solmization as a procedure for solving ficta occurrences at large—as illustrated in another

statement by Margaret Bent.

It [i.e., hexachordal solmization] cannot in itself solve individual ficta problems just as,

conversely, no ficta solution can be rejected on grounds that it can't be solmized.

(Bent 1996, § 18)

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While neither she nor other authors dismiss solmization as an analytical tool, they

have not underscored its role regarding musica ficta (both as determinant and as means). In

my opinion, such positions arise from a reluctance to exercise reading procedures based on

hexachordal models (rather than octave ones), and from a tendency to interpret musica ficta

mainly within its polyphonic contexts (as if it was the product of and particular to those

contexts). Moreover, modern scholars have not provided close interpretive readings of

historical texts with respect to their rhetorical and philosophical substrata, and have chosen

to grant excessive weight to those passages that, prone to purely technico-pedagogical

understandings, are able to generate clear-cut rules and terminology. As a result, many of

the so-called 'rules of musica ficta ' (according to modern scholarship) have been based on

contrapuntal concerns, particularly causa necessitatis ('for the sake of necessity') and causa

pulchritudinis ('for the sake of beauty'), as commonly understood. I will argue, however,

that most of the basic concepts of musica ficta were already applied consistently to

monophonic music, and were initially more dependent on the understanding of solmization

and of purely melodic contexts (over which the individual performer had greatest control),

than on polyphonic/contrapuntal ones (properly controlled by composers, theorists, or

perhaps even scribes).2

2 The monograph by Thomas Brothers (1997), and the articles by Albert Seay (1969) and by

Karl-Werner Gümpel (1990) present invaluable concepts and interpretations to the use of musica ficta

within monophonic contexts, although the significance of the latter two have been apparently overlooked

by many scholars, and despite Brothers's declared resistance to solmization as a main tool for analysis.

xxvii

Determining the moment in modern scholarship when the role of solmization seems

to have been devalued is not the specific concern of this dissertation. One must observe,

however, that even before such influential and reputable studies on musica ficta as the most

recent ones by Karol Berger (1987) and by Thomas Brothers (1997), other scholars shared

a tendency to understand and transcribe ficta-signs as mere accidental inflections

(corresponding to our modern flats and sharps), with the exception of the sign on the

f"-position, called 'extra manum' ('beyond the hand')—i.e., 'beyond the established gamut'.3

This approach disregards (consciously or not) the primary function of all -signs, which is

to enforce a solmization-syllable (fa), and not to indicate any specific pitch or accidental.

Karol Berger does state that musica ficta occurs when solmization syllables are feigned, that

is, when one employs steps that fall outside the medieval (Guidonian-inspired) 'gamut', or

that are necessarily solmized with a syllable not assigned to them in that 'gamut'. Yet, he

ultimately interprets the ficta-signs themselves as accidental inflections, as rather

conspicuously emphasized in his title (Musica ficta: Theories of Accidental Inflections in

Vocal Polyphony).

Brothers's title also broadcasts an understanding of ficta-signs in line with our

modern concept of accidental inflections. In his Chromatic Beauty in the Late Medieval

Chanson: An Interpretation of Manuscript Accidentals, Brothers rejects solmization as a

3 Scholars have interpreted the term 'hand' (i.e., the 'Guidonian hand', in its musico-technical

medieval context) both as a graphical representation and technical reference to the standardized medieval step

system (modernly called 'Guidonian gamut', or simply 'gamut'). Thus, the term 'hand' ('manus') denotes the

limits of the gamut from G to e" (or, in post-Guidonian nomenclature, from Γ-ut to ee-la), in which steps

were assigned to the joints, pads, and fingertips of the palm—cf. (NG 1, 17: 458–9; New Harvard, 356).

xxviii

foundation for the interpretation of ficta in thirteenth- and fourteenth-century music.4 One

of the texts on which he bases his case is drawn from Walter Odington's Summa de

speculatione musice (first half of the fourteenth century). The passage is both rhetorically

and philosophically quite rich; it is also straightforward, systematic, and didactic, and these

features have given it some prominence in the writings of many scholars of ficta, since it

provides a useful basis for laying out 'rules' for a technico-pedagogical approach.

Brothers's conclusions are based, however, on a particular reading of Odington's text.

Due autem voces mobiles, scilicet b acuta et

bb superacuta sunt proprie voces monocordi;

reliquas vero vocant falsas musici, non quod

dissone sint, sed extranee, et apud antiquos

inusitate.

(Odington in. 14th cent., pt. 5, ch. 4;

CS 1: 216; Corpus Scriptorum de Musica

14: 98)

These two changeable tones, b and bb, are

called proper degrees of the monochord;

however, the rest of the changeable tones are

called false music, not because they are

dissonant, but because they are outside [of

the regular disposition of the monochord]

and were not used by the ancients.

(Brothers 1997, 2–3)

Brothers's understanding (apparent from his translation and bracketed insertions),

forms part of the conceptual background for his contention that musica ficta could not have

been used in any manifested accord with solmization, because it was simply "not used by

the ancients." For him, musica falsa or ficta had not been successfully integrated with the

theoretical foundation for the use of hexachords, or with the explanations of the medieval

4 Conflicting with my understanding of Berger's work, Brothers reads Berger as a defender of

solmization, and remarks that:

[Karol Berger's interpretation] puts an emphasis on solmization that I would resist. At the very

least, it should be observed that this point of view does not ring true for the thirteenth and

fourteenth centuries.

(Brothers 1997, 2 n.4)

xxix

gamut.5 But his interpretation does not reflect the original meaning of this particular

quotation which might be better (and more literally) represented by the following

translation.

Now, two mobile steps, namely and , are properly [called] steps of the monochord; the

remaining [mobile steps], however, are called musicas falsas, not because they may be dissonant,

but [because they are] from outside [the monochord], and among the ancients [are said to be]

unusually [constituted].

(my translation)

In many instances my choice of words does not appear to differ significantly from

Brothers's translation (e.g., "mobile" instead of his "changeable"), but such nuances are

often necessary to preserve the clarity and precision of the original text, as well as its

metaphors and ambiguities. It is fairly clear that "inusitate" cannot stand for "not used" (as

Brothers would have it), but rather denotes 'out of the ordinary', 'unusual', 'scarcely used', or

simply 'not preferred', even if used when necessary or fit. Reading Odington's text beyond

5 Commenting upon Anonymous 2's use of the word "beauty" in relation to musica ficta and to

the so-called "cantinelli coronati," Brothers says:

[T]he larger context of this passage suggests that the theorist uses the word not in the sense of

systematic regard for rational order but, rather, just the opposite, as a way of valuing departure

from such systematic ordering.

[...] It is easy to ground the necessity rule i the codifications of music theory, which pays attention

to the measurement of the vertical intervals. For monophony, that grounding is not so easy; to

the contrary, with monophony, musica ficta more obviously violates modality and hexachordal

organization of pitch. If the application of musica ficta in monophony cannot be easily integrated

with theory, what better way to justify it than by simply acknowledging the potential for beauty?

(Brothers 1977, 4–5)

In this dissertation I hope to demonstrate that musica ficta, hexachordal structures, and solmization

procedures are not only compatible, but that the use of musica ficta depends on the proper understanding and

practice of those organizations in medieval theory.

xxx

the limits of Brother's extracted quotation reveals that the "remaining [steps]" refer

exclusively to E , f , c ', e ', and f '—an understanding that Brothers seems to have

overlooked, for he takes the phrase to embrace the entire set of all possible ficta-steps (i.e.,

of the entire ficta-gamut).

My approach to this passage (and others from historical treatises which I will treat

in close detail) exemplifies three interpretive or exegetical methodologies which will be

called upon in my work. First, the interpretation of what Odington means by "remaining

[steps]" (according to my translation for "reliquas [voces]") depends on information stated

in other parts of his text, as seen above. This kind of interpretation (whether derived from

explicit or implicit content of Odington's treatise) constitutes what may be called a

'denotation' or, as formal logic names it, an 'extensional' interpretation. Second, the

interpretation of a term or expression such as "inusitate" may or may not depend on what is

explicitly stated in the text. It will, however, depend on the status of the term, situation, or

description to which it refers (as represented in the previous paragraph by my interpretation

of the term "inusitate"). This second approach (or 'intensional' interpretation) is constituted

through 'connotation'; one of its characteristics is that it may result in either technical,

non-technical (say, a social or cultural interpretation related to the reconstruction of some

shared understanding, contemporaneous with the text), or both types of 'reading'. Third, the

interpretation of terms that yield to nuances (e.g., "voces mobiles") usually depends as

much on non-literal as on literal meanings, and also illuminates both technical and

non-technical aspects of a text's content. The difference between the second and third mode

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of approach is that in the latter, full comprehension of technical aspects is dependent on

assessments of the other parameters. For the purposes of this dissertation, this third

interpretive approach will be called a 'socio-rhetorical' interpretation, and its intent is to

establish definitions as well as relations between text signifiers and signifieds, all informed

by both technical, rhetorical and philosophical aspects. I have avoided the term

'semiological' interpretation, since technical linguistic analysis is not the object of this

dissertation.

At the same time, no study has yet been dedicated to investigating the rich

philosophical and socio-historical implications of the highly charged language of ficta

theory, specifically its reliance on qualitative terminology such as 'false, true, fictive, real,

vice, etc.' By way of example, it seems appropriate to present a quotation drawn from the

treatise entitled Scolica enchiriadis—which served as the original stimulus for my

exploration of this dissertation topic.

D[iscipulus]. Quomodo fit haec absonia in

ptongis?

D[isciple]. In which way do these discordant

things occur in the phthongi?

M[agister]. Si aut ignavius pronuntientur

aut acutius, quam oportet. Primo namque

hoc vitio in humanis vocibus et sonorum

qualitas et tota leditur cantilena. Quod fit,

ubi, quod canitur, aut segni remissione

gravescit aut non rite in sursum cogitur.

Quod vitium in quibuslibet musicis

instrumentis nequit fieri, eo quod disposito

semel ptongorum ordine vox sua sonis

singulis manet. Alia fit dissonantia, quando

sonus a sono falso metitur, id est alius pro

alio. Tertia dissonantia, quando sonus non

M[aster]. If they are pronounced either lazier

or more energetically, than it is proper.

First, because by this vice in human voices,

both the quality of sounds and the whole

song (cantilena, i.e., plainchant) is harmed.

That happens whereby what is sung either

gets worse by idle remission, or is unfitly

imagined upwards (that is, 'unfit' to

religious usage). That vice is incapable of

occurring with any one musical instruments;

because the voice [of the instrument]

remains with its own individual sound, once

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respondet sono, quoto loco oportet. Et haec

duo vitia ex eadem quidem causa nascuntur;

sed in hoc differunt, quod illud in eadem fit

neuma, hoc vero in praecinendo et

respondendo.

(Anon. SE a. 900, pt. 1; Schmid 1981,

61–62; cf. also GS 1: 173–174; PL 132:

983)

it has been arranged in order of phthongi.

Another dissonance occurs, when the sound

is measured by [means of] a false sound, that

is, [when] one [sound is mistaken] by

another [different sound]. A third dissonance

[occurs], when one sound does not answer to

[another] sound, in the place where it is

proper. And these two vices, indeed, spring

from the same cause; although they differ in

this, that the former occurs in the same

neuma (i.e., within a melisma of a chant),

[while] in fact, the latter [occurs] in singing

and answering (i.e., in monophonic

passages such as in responsories or

antiphons, or in polyphonic passages such

as in organa).

(my translation; cf. also Erickson 1995, 34)

As Margaret Bent has pointed out (NG 1, 12: 803; NG 2e, s.v. 'Musica ficta,' §2.i),

the word vitium ('vice') is among the first terms employed to indicate a kind of practice that

would later be described as musica ficta, or musica falsa—the latter being a term "more

common in the 13th century" (NG 1,12: 802). The word vitium, literally meaning 'fault' or

'defect', but also 'vice', 'sin', and 'corruption', clearly points to concepts and metaphors that

relate to the idea of social structures and norms (whether manifested in ethics, politics,

theology, rhetoric, or in other disciplinary approaches).6 It has been generally accepted that

6 Among the earliest treatises that made use of the word "vitium" (or of its derivative

declensions or adjectives), within the context of musica ficta, one can find the following: Scolica enchiriadis

(Anon. SE a. 900, pt. 1; GS 1: 173–174, 175, 177; PL 132: 983, 985, 987; Schmid 1981, 61–62, 65,

70–72); Alia musica (Anon. Alia mus. ca. 890, [chs. 19–20]; Heard 1966, 197, 199; GS 1: 140; PL 132:

945; Chailley 1965, 193, 203); two, apparently related treatises whose author(s) was (were) formerly

identified as Odo, one entitled Dialogus de musica (Ps.-Odo ex. 10th cent. D; GS 1: 251, 263, 264; PL

133: 757, 758, 771, 772), and the other entitled Musicae artis disciplina (Ps.-Odo ex. 10th cent. M; GS 1:

272; PL 133: 781); Tonarius (Odo d'Arezzo ex. 10th cent., preface; GS 1: 249; PL 133: 756): Prologus in

Tonarium (Berno Augensis p. 1021, chs. 9, 11, 14; GS 2: 73, 74, 77; PL 142: 1110, 1111, 1114); De

xxxiii

both terms (vitium and the later musica ficta) were presented in association with polyphonic

contexts, and linked specifically to polyphonic practice and performance, and the relations

between voices. However obvious the association with polyphony turns out to be, the

association with plainchant practice and transmission cannot be dismissed. It is my

contention that the word vitium can also be associated with plainchant-'corruption' (of the

kind due, perhaps, to malpractice or transmission), and that such an association establishes a

link to the 'corruption' of individual voices in plainchant and in polyphony. For this, the

contemporaneous language of social relationships and aggregations of each time period, and

perhaps their political or ethical strictures, must be taken into consideration, in order to

attempt a deeper and more historically apposite understanding of the meanings and context

of musica ficta.

This approach extends beyond the purely technical to the metaphysical, just as social

relations and the medieval concern with individuation were also matters of metaphysics.

Indeed, if the use of ficta stands as a metaphor for certain social phenomena, then the proper

use of a ficta-sign might be determined, or at least suggested, not only by theoretical rules,

but also by determination of its correspondent social relation(s). In a polyphonic setting,

each voice could be understood as a single individual (or even as a distinct group of similar

individuals). One voice would then relate to the other(s) in a way that reflects (or could

musica (Hermannus Contractus a. 1054; GS 2: 140, 144; PL 143: 430, 433); De musica (Aribo

Scholasticus ca. 1070's; GS 2: 198, 203, 225; PL 150: 1308, 1313, 1341; Smits van Waesberghe 1951b,

2, 14, 47); De musica cum tonario (Affligemensis ca. 1100, chs. 14, 15, 18, 22; GS 2: 248, 249,

253–254, 260–261, 263; PL 150: 1411, 1418, 1425–1426, 1428; Smits van Waesberghe 1950, 101, 104,

118–119, 142, 146, 156).

xxxiv

reflect) the relation between two individuals within a given society. Such a metaphor is

expressly set forth in Nicole Oresme's fourteenth-century treatise on currency, in which an

ethical prince stands at the center of societal harmony as the tenor stands as the foundation

of a polyphonic musical structure, with the other voice parts standing for the well-balanced

and properly functioning society.7 We might extend the basic metaphor with reference to

specific styles of polyphonic relations (imitation, homophony, etc.). Societal balance, like

music, may be disrupted by dissonant clashes. In order to restore the stability of relations at

large, or resolve the clash between individuals, the dissonance may (or may not) be changed

into a consonance by means of musica ficta (i.e., by means of 'vices'). Moreover, as stated

in Scolica enchiriadis, those vitia in music should be understood "just as [the rhetorical

'vices' called] barbarisms and solecisms" (Vitia nimirum sunt, sed sicut barbarismi et

soloecismi).8 Whether the compromising voice performs a 'vice' or sings 'falsely' or

'fictively,' the terms and the act they represent—set in motion by a stronger and apparently

intractable agent—bear both ethical and political implications, related (as I hope to

demonstrate) to the language of Classical and medieval philosophy and rhetoric.

7 Michael Long has discussed this aspect of Oresme's translation and commentary on De moneta

in "The Clink of Coin: Musical Structure and Hard Currency in 14th-Century Europe," paper delivered at

the International Musicological Society Congress, Leuven, Belgium, August, 2002.

8 Cf. (Anon. SE a. 900, pt. 1; Schmid 1995, 70; GS 1: 177; PL 132: 987; [trans.] Erickson

1995, 41; cf. Atkinson 1988, 194)—this fragment is quoted in a more contextualized passage in chapter 8 .

xxxv

SUMMARY OF CHAPTERS

Chapter 1 – The Gamut, Musica Vera and Musica Ficta

This chapter undertakes an overview of the Medieval Gamut and its relations to the

terms Musica Recta and Musica Ficta. It consists of a brief presentation of the

Medieval Gamut with regard to its range and solmization-syllables, and their use in

both musica practica and in musica speculativa, mainly based on the Guidonian

tradition inherited and followed by later authors, and leading to the expansion of its

limits toward what is today called musica ficta. The main purpose is to introduce

some basic concepts and terminological items used in the course of the dissertation.

Most of the material here presented has already been subjected to the scrutiny of

several scholars, and is generally known among musicologists. This chapter,

however, will offer some new approaches, close readings, focus on details, and on

terminological definitions that are particular to this dissertation, providing

background information to the understanding of what musica ficta is, and how it

works.

xxxvi

Chapter 2 – Principles of Hexachordal Solmization

First, terms such as deductio and proprietas will be defined in the context of

Guidonian solmization and its predominance (considering both musica practica and

speculativa). Following, instructions will be presented on how to identify

hexachords, and how to solmize a piece of music, both according to different levels

of learning (as they were identified in historical treatises), and to melodic gestures

that serve as indications of hexachordal structures. Additionally, I will introduce the

concept of the octave equivalence between hexachords, which is not explicitly stated

in medieval or Renaissance treatises. Nevertheless, there are situations in which the

equivalence will be shown as inevitably practiced and implicitly understood. Finally,

there will be a brief discussion about speculative evidence in theoretical works that

oppose the use of the Guidonian hexachordal paradigm for solmization.

Chapter 3 – Mutation: The Basics

This chapter discusses 'mutation' by means of statements in a number of historical

treatises, presenting its concepts and cases ('explicit' and 'implicit' mutation), as well

as a subcase of the latter (named 'indirect' mutation in this dissertation). As the most

basic procedure of hexachordal change, mutation is also the conceptual basis that

permits the integration of musica ficta into the restricted recta-gamut, since ficta is

also a practice that implies change. This chapter will also introduced the terms

xxxvii

'mutated'-syllable and 'mutant'-syllable, following statements given in historical

treatises. Additionally, a few instances that relate mutation to rhetoric will be

inspected, introducing background information for the discussions undertaken in

chapter 7.

Chapter 4 – Mutation: 'Irregular' Type, 'Ficta' Species, and Position ofFicta-signs

Continuing with the discussion started in the previous chapter, a different types of

mutation ('irregular') will be examined together with the species called

'ficta'-mutation. Nuances between them and their counterparts ('regular' and 'recta'

mutations) will also be discussed, together with the function of ficta-signs relative to

their physical position within the music, demonstrating their primary function as

enforcers of specific hexachordal solmizations.

Chapter 5 – Permutation

'Permutation' will be shown as a procedure capable of implementing abrupt shifts

between hexachords, since it involves a motion between two notes that pertain

exclusively to different hexachords. Examples of emblematic situations that require

the use of 'permutation' are cases of chromatic stepwise inflection and dissonant

leaps (such as tritones); these will be discussed individually. Other cases that invite

xxxviii

a 'permutation' are leaps in which two hexachords are not promptly indicated, but

which can generally be solmized by means of alternative solmizations that allow for

certain kinds of mutations (according to what was seen in chapters 3 and 4). Since

it is one of the most difficult procedures, it was not discussed by many authors of

historical treatises.

Chapter 6 – Transmutation

'Transmutation' is the last procedure of hexachordal change to be discussed, and as

the other two procedures it also includes different cases, such as the upper-semitone

inflections (or upper-neighbor note) represented by fa-super-la situations, and

subsemitone inflections. The latter is usually related to polyphonic contexts by

means of 'propinquity' motions dictated by counterpoint (at least since the fourteenth

century), but may be found in purely monophonic contexts as well. In this chapter

(also as done in previous chapters), relationships between specific cases of

transmutation and selected rhetorical figures will also be explained. The term

'transmutation' is in fact a proposition given in this dissertation as an umbrella term

that encompasses particular momentary inflections that fall outside a given

predominant hexachord, but return to it without promoting its decharacterization.

xxxix

Chapter 7 – Figures of Solmization and Figures of Rhetoric: The musicaldiscourse

This chapter will be entirely dedicated to tracing several relationships between the

three basic procedures of hexachordal change (mutation, permutation, and

transmutation) and basic concepts and figures of rhetoric (especially metaphor,

allegory, and metonymy). Although parallels will be traced between these

procedures and figures, relationships with other figures will also be inspected,

following the concepts exposed in previous chapters. The objective is to broaden

the scope of understanding about these procedures as they are implemented in

practice and as they are discussed in theory.

Chapter 8 – Terminological Issues: Forging Terms, Definitions, and Conceptsin Modern Scholarship

This chapter will be dedicated to discussing and analyzing basic definitions of

musica ficta and the application of ficta-signs as a generic term for mi- and fa-signs.

Modern scholarship has interpreted that different rules (and their underlying

conceptualizations) were meant for different audiences. In light of this, definitions

and concepts of basic definitions of musica ficta will consider enunciations and

understandings in modern scholarship, as well as evidences contained in early music

theory. The adoption of the term 'ficta-signs', preferred in this work instead of

'accidentals' or any other alternative, will be discussed and justified on the basis of

xl

philosophical and rhetorical grounds, as well as on usage and functions of the

'signs', as explained in previous chapters.

xli

— CHAPTER 1 —

THE GAMUT, MUSICA FICTA AND MUSICA RECTA

(i) The Gamut: A Presentation and Overview

The medieval system (gamut) was the result of a gradual manipulation that

culminated in works from the end of the tenth century and early eleventh century, in

particular Pseudo-Odo's treatise Dialogus de musica (ex. 10th cent. D) and Guido

d'Arezzo's writings (datable to ca. 1020's-1030's).9 Toward the end of the twelfth century,

the system (as presented in FIG . 1 .1 below) had settled and, once that happened, was

maintained (virtually unaltered) up to the sixteenth century—the additions proposed in this

period (especially those during the Renaissance) were usually presented as expansions of

an otherwise well-established system.10 The system was mainly designed to render

9 The author of the Dialogus de musica, here mentioned as Pseudo-Odo, has been once attributed

to Odo of Cluny (GS 1: [d4 r], 251; SR 1950, 103), and has more recently been declared to be anonymous,

or even authored by a certain Odo d'Arezzo. The treatise may also be divided into two parts: its prologue,

and the treatise itself—these seem to have been written independently, probably by two different anonymous

authors. References in (Jacobsthal 1897, 228; Huglo 1969; 1971; SR 1998; 198–199).

10 Previous attempts to supply adequate identification, expansion, and establishment of such a

system (notedly applied to the plainchant repertoire) can be traced back to Hucbald's De musica [formerly

called De harmonica institutione] (ca. 900), and the anonymous treatises Musica enchiriadis and Scolica

enchiriadis (both written before 900). It is noteworthy that these late ninth- or early tenth-century treatises

1

theoretical explanations (inherited through Boethius) adequate to the needs and features of

musical practice, especially that related to the plainchant repertoire. While borrowing

preexisting means (useful to performers) for learning and reading music, it also provided a

vocabulary of step-designations for use in theoretical discussions.

(pitches)Modern System

G

Γ

7 : .6 : .5 : .4 : .3 : .2 : .1 : ut

A

A

.

.

.

.

.

.re

B

B

.

.

.

.

.

.mi

c

C

.

.

.

.

.utfa

Graves

d

D

.

.

.

.

.resol

e

E

.

.

.

.

.mila

f

F

.

.

.

.utfa|

g

G

.

.

.utresol|

a

a

.

.

.remila|

b

.

.

.

.fa||

b

.

.

.mi|||

.

.

.

Acutae

c'

c

.

.utfasol||

d'

d

.

.resolla||

e'

e

.

.mila|||

f'

f

.utfa||||

g'

g

utresol||||

a'

aa

remila||||

b '

.fa|||||

Superacutae

b '

mi||||||

c"

cc

fasol|||||

d"

dd

solla|||||

e"

ee

la||||||

FIGURE 1 . 1 - Recta-Gamut (post-Guido d'Arezzo)

Medieval System(steps: letters plus hexachord-syllables)

have also been credited as being the earliest sources containing discussions on a number of fundamental

matters in Western music: beginnings of a true diastematic notation, descriptions of modes according to

their finales and their ambitus, descriptions of polyphonic singing, and (in the case of Hucbald's treatise) a

systematic and definite integration of the synemmenon tetrachord into the system, merging the Greater and

Lesser Perfect Systems (although with deviations from the Greek model)— (Babb 1978, 7–9, 29–39;

NG 1, 8: 758–759, s.v. 'Hucbald'; Phillips 1984, 1–2, 120–162; Erickson 1995, xx–xxii, xxiv–xxxvi;

NG 2e, s.v. 'Hucbald of St. Amand,' access 8/21/2003). Guido's own range (only up to dd—i.e.,

modern d") and use of syllables for teaching music will be discussed below in this chapter, but it must be

noted that the few additions and variants implemented thereafter did not impose significant changes or

departures from Guido's model, either with respect to range or designation for each step.

2

As the extant historical treatises reveal, the most standard learning/reading practice

(i.e., 'solmization') that survived through the Middle Ages and Renaissance was the one

associated with Guido d'Arezzo (* ca. 991/2 – † p. 1033) and his pedagogical ideas.11

Step-syllables (ut, re, mi, fa, sol, la) were proposed by Guido for solmization, and theorists

used identifications (designations) that merged the step-letters (from Γ to ee, or in modern

terminology from G to e"), derived from Pseudo-Odo's propositions, with those

syllables—e.g., Γ-ut (i.e., Gamma-ut, for our modern pitch G), c-sol-fa-ut (for c').12

Regarding the step-letters, the Dialogus has been deemed the first work to

successfully describe musical divisions in an 'ascending' scale-like manner imposed upon

the monochord.13 The divisions were calculated, presented, and defined according to a

stepwise scheme, from A to aa (including Γ as the whole, free string of the monochord),

providing the idea that basic intervals started with the tone and semitone, and only after

proceeding to the diatessaron, diapente, diapason, and the ditone (i.e., fourth, fifth, octave,

and major third). This kind of division has been identified as a design proper to musica

practica treatises, whereas in more pure musica speculativa treatises presentations of

11 In this dissertation, the term 'solmization' (from the Latin 'solmisatio ') is reserved for the

medieval and Renaissance activity of learning and reading music, and 'solfege,' for the modern one.

12 In the present work, the term 'step' has been chosen to denote individual letter-plus-syllable

designations, following medieval and Renaissance practice, whereas 'pitch' has been reserved for letter-only

designations, following modern patterns and concepts. In this dissertation, modern pitch-letters appear in

boldface, medieval step-letters appear in regular typeface, and step-syllables, in italics—FIG. 1 . 1 .

13 Chapters 2–4 in the Dialogus—(Pseudo-Odo ex. 10th cent. D, chs. 2–4; GS 1: 253–255;

PL 133: 760–763; (trans.) SR 1950, 105–109; SR 1998, 201–204).

3

monochordal divisions started with the diapason and bis-diapason (i.e., double-octave),

then proceeding to diapente and diatessaron, and only after deducing the tone, etc.—this

latter type has thus been named 'descending.'14

Following Boethius's transmission of Greek tradition, the monochord seems to have

been used mainly for speculative pedagogical purposes, i.e., calculations of both a

mathematical and acoustical nature which served to demonstrate the numerical and intervallic

relations between their proportions. However, it had also served practical purposes even

before the Dialogus: the monochord was used as an instrument for the primary teaching of

music to performers, and possibly as a performing instrument. Despite the apparent

independence promoted by the abstract, Guidonian-based model of solmization (which shall

be explained in detail in the course of this dissertation), the monochord was still maintained

as a primary, rather than auxiliary, pedagogical device.15 With the calculations on the

monochord facilitated by the Dialogus, and the assimilation of Guidonian solmization, the

monochord took on the additional function of a musical 'ruler,' i.e., a device that could be

used for checking the correct intonation of specific intervals learned by other means.16

Although in many previous treatises the main object of discourse was that of

theoretical speculation, generally with little regard to the performer, Pseudo-Odo's Dialogus

14 Terminology according to Cecil Adkins (1963, 78–80; 1967, 39–41).

15 In accordance with the interpretations of Cecil Adkins (1963, 337–372; 1967, 36, 43).

16 The function of the monochord as a performing instrument is still debatable, but it may be

noted that, in the famous Le voir dit, Guillaume de Machaut gives a list of instruments that appeared in a

performance to which he attended. The monochord is given among the listed instruments.

4

de musica (ex. 10th cent. D) displays a marked concern with the practice of music. The

purpose of the treatise was itself pedagogical: it aimed to instruct performers, thus

preventing further corruption of the repertoire and allowing for its correction as well.

Sollicite quoque ac curiose investigantibus,

an per omnes cantus nostra valeret doctrina,

assumpto quodam fratre, qui ad

comparationem aliorum cantorum videbatur

perfectus, antiphonarium sancti Gregorii

diligentissime investigavi, in quo pene

omnia regulariter stare inveni. Pauca vero,

quae ab imperitis cantoribus erant vitiata,

non minus aliquorum cantorum testimonio,

quam regulae sunt auctoritate correpta.

(Pseudo-Odo ex. 10th cent. D; GS 1: 251;

PL 133: 758)

When you earnestly and diligently inquired

whether our doctrines would be of value for

all melodies, I took as my helper a certain

brother who seemed perfect in comparison

with other singers, and I investigated the

Antiphoner of the blessed Gregory, where I

found that nearly everything was accurately

recorded. A few items, corrupted by

unskilled singers, were corrected, both on

the evidence of other singers and by the

authority of the rules.

(SR 1998, 199; cf. SR 1950, 104)

As shown in the quotation above (from the prologue of Pseudo-Odo's treatise), the

author ascertains that the musical rules and their establishment ("doctrina") are to be

justified and checked by practice (i.e., by fidelity to the musical text of plainchant). It is

consistent with these concepts that Guido d'Arezzo devised a method of solmization that

could enable memorization and consequent reproduction of two basic intervals: the whole

tone (T), and the semitone (S). The method—adopted by the majority of medieval and

Renaissance practical musicians (especially, but not exclusively, singers) —was built upon

hexachords of the same structure and specific solmizations syllables were attached to each

step of the hexachord. The basic intervallic structure of the model hexachord was

T-T-S-T-T, and its correspondent solmization syllables (ut, re, mi, fa, sol, la) were

acrostically drawn from the first syllable of each half-line of the hymn to St. John "Ut

queant laxis"—FIG . 1 .2 .

5

| |

|

| | !

8 Ut que-ant la – xis re -so-na - re fi-bris Mi – – ra

8 ges - to – rum fa -mu - li tu – o -rum, Sol – – ve

8 pol -lu - ti la - bi - i re - a – tum, San – cte Jo-han-nes.

FIGURE 1 . 2 - "Ut queant laxis" (Hymnus - mode 2). From (Pesce 1999, 466;

cf. LU, 1504). -hexachord (i.e., hexachord naturale).

The syllables themselves did not indicate fixed pitches (nor did the Pseudo-Odonian

step-letters, for that matter), but rather intervals (i.e., tones and semitones) within a six-step

diatonic span (hexachord). The interval of a tone would occur between any two consecutive

syllables, except between mi and fa, where there should always be a semitone.17

17 In Guido's original version, incidentally the solmization syllables ut, re, mi , fa, sol, la fell

respectively under the pitches c, d, e, f, g , and a. Though the Hymn to St. John may have been

pedagogically useful, it has also been deemed unidiomatic in terms of plainchant. The text for the "Ut

queant laxis" hymn probably dates from the eighth or ninth century, and Guido may have made changes to a

previously known melody, or possibly composed it anew—since his Epistola ad Michahelem (ca. 1032) is

probably the first document to mention and present such a melody. The correlation between the Guidonian

syllables and the pitches from c to a is especially significant because virtually the same syllables are used

in the modern fixed-do system of solfege and of pitch identification—largely accepted and practiced in most

occidental countries. (The movable-do system of solfege, and the identification solely by means of

pitch-letters has been characteristic only within the German and English traditions.) Nevertheless, there are

a few manuscripts that present the hymnal melody in a transposed version, beginning on Γ-ut (G) instead of

on C-ut (c)—a summary is presented in chapter 2 (iii). For opinions of scholars concerning these matters,

cf. (Oesch 1954, 66–67; Pesce 1999, 19–38, 547–548; NG 2e, s.v. 'Guido D'Arezzo,' access 1/15/2004);

for reproductions of the Ut queant melody, cf. (GS 2: 45; PL 141: 425; Pesce 1999, 466, 549–554). In

6

For any given melody, if the range was that of a major 6th or less, and the intervallic

structure (configuration) of that span could be matched to the one proposed in Guido's

hexachord, then only one underlying hexachord would be represented and would be enough

for its solmization. If, however, the melody did not follow that configuration, and/or the

range fell beyond a major 6th, then the solmization could be effected only by a series of

hexachords properly interlocked. This is a more specific understanding of the term

'solmization,' which has been linked more generally to the activity of learning and reading

(or imagining) music, generally by means of the Guidonian-based hexachord syllables (ut,

re, mi, fa, sol, la) not as indicators of specific step-letters or pitches since it is a movable

method; hexachordal solmization will be discussed in subsequent chapters.18

Pesce's edition/translation of the Epistola, the second verse of the hymn is given in the following manner:

"Mira gestorum, famili tuorum" (instead of "famuli")—there is, however, no mention or explanation

regarding such a change of spelling, cf. (Pesce 1999, 466–467, 547–548, 551).

18 Though the terms 'solmization' and 'solfege' are both found in medieval (as well as

Renaissance) treatises through the words 'solmisatio ' and 'solfisatio,' the modern term 'solfege' has been

related to a practice that is quite different from that applied (in modern times) to 'solmization.' 'Solfege' is

also meant as a learning and reading activity that, though influenced by the Guidonian tradition, has

expanded the hexachord-set to include seven syllables (i.e., an heptachord), which do individually account for

specific pitches when the fixed-do method is employed (or even when the learning/reading is done via

pitch-letters). The extra syllable of this heptachordal system, designated si in the modern fixed-do method

(and turned to ti in the modern movable-do method), was justified as a deduction from the initial letters of

the words S ancte Iohannes (from the Hymn to Saint John), and was probably devised within the French

tradition, as attested by Janowka in his Clavis ad thesaurum (Janowka 1701, 119, s.v. 'Solmizatio')—cf.

(NG 1, 14: 788, s.v. 'Pitch notation'; NG 2e, s.v. 'Pitch notation,' access 1/14/2004). The syllable si has

then been attached to the pitch-class , and the syllable do, attached to , has gained widespread currency

instead of ut—except in the French tradition, where ut continues to be used. (Further assessments and a

survey of the actual use of the Latin word solmisatio and related terms—e.g., solfisatio—are given later in

chapter 8 .)

7

The alphabetical indication of steps (i.e., step-letters) can be traced back to the Greek

tradition, from which Boethius derived his own letter designations in De institutione musica

(ex. 6th cent.), which in turn informed later works—e.g., Hucbald's De musica (ca. 900).19

But it was only with Pseudo-Odo's Dialogus (ex. 10th cent. D) that a sequence with

step-letters from A through G (repeating the same order at the octave) was proposed and

later canonized; a proposition that imprinted a musica practica character on the system.

This Pseudo-Odonian model was used by Guido as a foundation for several of his own

propositions, although it was still dependent on the Greek model and was limited to the span

from Γ to a, i.e., from G to a', where a' was regarded as the highest sound (corresponding to

the Greek nete hyperbolaion). Guido is credited with extending the system at least up to dd

(d"); ee (e") is likely an even later addition to the system.20 Also, the presence of a pitch

19 According to Duchez (1979, 166–167), the study of Boethius's musical treatise apparently

began only shortly before the mid-ninth century. In this light, Hucbald's treatise may be rendered possibly

as one of the first works to follow and promote the ideas of Boethius, at least with respect to step-letter

designations, even if deviating from that model.

20 In his Micrologus (ca. 1026–28), Guido implies that the four steps he was adding (the

superacutae , , cc, dd) were already being used in practice, even if considered superfluous. Even in the

manuscript F-Pn lat. 7211, a twelfth-century copy of Guido's Epistola ad Michahelem (ca. 1032), although

there is a hexachord based on g', the pitch e" (equivalent to the step ee-la) is not present, thus making that

particular hexachord incomplete—cf. FIG. 1 . 1 , and (Santosuosso 1991) for a copy of the relevant passages

in manuscript F-Pn lat. 7211 (f. 99v–100r). For some of the relevant sections concerning extension (or

even restrictions) of the gamut within Guido's propositions, see his Micrologus (Guido d'Arezzo

ca. 1026–28, ch. 2; B-Br II 784, f. 3v; GS 2: 4; PL 141: 382; Smits van Waesberghe 1955, 93–95;

[trans.] Babb 1978, 59–60), and the Epistola (Guido d'Arezzo ca. 1032; F-Pn lat. 7211, ff. 99v–100r;

GS 2: 45–46, 48–49; PL 141: 425–426, 429–430; [trans.] SR 1950, 123–124; [trans.] SR 1998, 217;

[ed. and trans.] Pesce 1999, 462–479, 508–517)—some commentaries on these subjects, as they appear in

the Micrologus and the Epistola, as well as in other treatises by Guido, may be found in (Babb 1978, 52;

NG 2e, s.v. 'Guido D'Arezzo,' access 1/14/2004; Pesce 1999, 25–29).

8

between a and b (that is, b ) had already been part of the Greek system (corresponding to

the trite synemmenon), and both Boethius and Hucbald, following that tradition, had

discussed the synemmenon tetrachord and its inclusion of a note equivalent to b (but not

b '). In Pseudo-Odo's Dialogus, however, the monochord was used to deduce F

(equivalent to f), from which proceeded the deduction of the step-letter (equivalent to b ),

thus justifying its presence not as a mere part of the synemmenon tetrachord, and defining it

as a fourth relative to F (anticipating its main function as -fa).21 It seems that the

step-letter (i.e., -fa, equivalent to b '—cf. FIG . 1 .1) was adopted into the theoretical

system on the authority of Guido's writings.22 With regard to the two varieties of 'b'

present in the medieval system, historical treatises identified them by means of assigning

different shapes to the letter itself (and also different syllables to each of them), as well as

21 Cf. Pseudo-Odo's Dialogus de musica (ex. 10th cent. D, ch. 2; GS 1: 253; PL 133: 761;

[trans.] SR 1950, 106; SR 1998, 202).

22 In fact, as a result of the parameters set by the daseian notation and the descriptions about

organum, both Musica and Scolica enchiriadis included pitch-equivalents that are not found in other treatises

that were largely dependent on Greek theory tradition (through descriptions based on the Greater and Lesser

Perfect Systems), or even in what later became the standard post-Guidonian gamut. Scolica gives an

example that includes pitches up to f " (according to Erickson's transcription and translation, but

mistakenly printed as f " in Strunk's version [SR 1950, 131]). Moreover, both Musica and Scolica

enchiriadis included the low B instead of the low B —the latter could be obtained (according to Scolica

enchiriadis) by means of a vitium (i.e., musica ficta). For the presence of pitches above d" in the

Enchiriadis treatises, see the Latin editions given in (GS 1: [ME] 162–164, [SE] 185–192; PL 132:

[ME] 969–972, [SE] 995–1004; Schmid 1981, [ME] 28–34, [SE] 92–106]); and the correspondent

translations given in (SR 1950, [SE] 128–134; Rosenstiel 1976, [ME] 15–18; Erickson 1995,

[ME] 16–19, [SE] 57–63). For the presence of pitches below A (correspondent to the proslambanomenos),

see the Latin editions given in (GS 1: [ME] 152–154, [SE] 174–175; PL 132: [ME] 957–960, [SE] 984;

Schmid 1981, [ME] 4–9, [SE] 63–65); and the correspondent translations given in (Rosenstiel 1976,

[ME] 1–3; Erickson 1995, [ME] 2–5, [SE] 35–36; SR 1998, [ME] 190–191).

9

different descriptions, designations, and concepts. One variety was represented by the sign

, and described as a 'round' or 'soft' form of the letter 'b' (i.e., a b-rotundum, or b-molle).

The other variety was represented by the sign , and described as a 'square' or 'hard' form of

the letter 'b' (i.e., a b-quadratum or -quadrum, or else b-durum). In terms of modern

pitch-equivalents, b corresponds to -rotundum (which represents the trite synemmenon

according to the Lesser Perfect System, or -fa according to the post-Guidonian designation

paradigm), whereas b corresponds to -quadratum (which represents the paramese

according to the Greater Perfect System, or -mi according to the post-Guidonian

designation paradigm).23 As will be seen later, treatises (especially those that followed the

Guidonian tradition) often used the merging designation fa mi in their discussions,

which of course referred not to one single step, but rather to the two steps that alternately

occupied the same place (locus) in the 'hand'—i.e., in the gamut.24

Although the solmization procedures and the entire concept of the medieval gamut

with its hexachordal syllables were based on Guido's writings (at least as attested by later

historical treatises), neither their implementation nor their originality can be unequivocally

23 In historical treatises, the step-letter 'b' could be presented with no special shapes/designs

differentiating between the two varieties. However, that would happen only when that 'b' was paired with a

correspondent step-syllable. Thus the designation -fa could be notated simply as b-fa, and -mi, simply as

b-mi. Also, it may be noted that treatises were not necessarily coherent (and frequently were not) in their

graphical design of b's.

24 Throughout the present work, the designation will be given in the form -fa / -mi, and will

be addressed as a 'double-step.'

10

credited to him.25 In fact, the use of hexachordal step-syllables was among the last known

propositions of Guido d'Arezzo, appearing only in his Epistola ad Michahelem

(ca. 1032)—probably his last work. In terms of solmization there were also other types and

sets of syllables proposed both before and after Guido d'Arezzo, and also others by Guido

himself.26 The 'ut, re, mi, fa, sol, la'-set of solmization syllables seems to represent only one

of several propositions appearing in Guido's Epistola ad Michahelem (ca. 1032). Among

the surviving forty-seven manuscripts that presented the usual set of solmization syllables,

nine contain another text ("Trinum et unum") set to the "Ut queant laxis" melody, showing

only one minor melodic variant for the word "intende" at the end of the third verse.27

Below, FIG . 1 .3 shows a setting of that alternative text ("Trinum et unum"), which yields the

syllable-set 'tri, pro, de, nos, te, ad.' The transcription is based on the twelfth-century

25 About these and other Guidonian propositions Claude V. Palisca states that "none of these

innovations can be securely attributed to him" (Babb 1978, 49)—for an overview and similar statements cf.

(Henderson 1969, 17–36; NG 1, 7: 805–807, s.v. 'Guido of Arezzo'; NG 2e, s.v. 'Guido of Arezzo,' access

1/14/2004).

26 Before Guido, syllable-sets that may have been considered for solmization were those applied

to tetrachordal structures. In the Greek tradition, one finds the tetrachord-based syllables τε−τα−τη−τω,

initially as transmitted by Aristides Quintilianus (ca. 400, bk. 2; [Greek and Latin texts] Meibom 1652, 2:

90–97; [comments and translation] Mathiesen 1983, 33–34, 53–55, 140–146; [comments] Henderson 1969,

9–17)—cf. also diagrams, text and commentaries with regard to the anonymous treatise edited by

J. Friedrich Bellermann (1841, 22–27, 80–81), where the same tetrachordal set is also discussed, although

with variants. One finds also the noeanne/noeagis sets of syllables, whose first source of transmission to

Western Europe was probably the work of Aurelianus Reomensis (Musica disciplina, ca. 840–50), and was,

in the words of Claude A. Palisca, "a system of solmization derived from the Byzantine intonations or

enechemata" (Babb 1978, 6)—cf. also (Bailey 1974, 5–15; Strunk 1977, 19–36; Babb 1978, 10; NHarvard

1986, 116-119, 263-264, 541, s.vv. 'Byzantine chant,' 'Echos,' 'Noeane, noeagis'; NG 1, 3: 553-566, 6:

163, 17: 458, s.vv. 'Byzantine rite, music of the,' 'Enechema,' 'Solmization').

27 Cf. Pesce (1999, 547–555).

11

manuscript F-Pn lat. 7211, in which the "Trinum et unum" example is preceded by a setting

of the "Ut queant laxis" hymn—both in heightened notation.28

!

Tri -num et u – num pro no -bis mi - se - ris

De – – um pre-ce – mur nos pu -ris men – ti -bus Te

ob -se -cra-mus ad pre-ces in - ten -de Do – mi - ne nos-tras.

FIGURE 1 . 3 - "Trinum et unum" from Guido d'Arezzo's Epistola ad Michahelem

(F-Pn lat. 7211, ff. 99v–100r), presented in the -hexachord (i.e.,

hexachord durum).

Although Guido d'Arezzo himself may well have composed the melody for the

preexistent text of the "Ut queant laxis" hymn, and proposed its subsequent pedagogical

use, the same cannot be assured with respect to its actual implementation, nor to the

28 Henderson (1969, 20–26) provides a description of syllable-sets in fifteen manuscripts (from

mid-eleventh to the end of the twelfth century) that contain the Epistola. In these manuscripts, five provide

settings to the "trinum et unum," and one (F-Pn lat. 7211) includes a setting of yet another (shorter) text

(also to a different and shorter melody). The text is: "Trinitas protege Deus nos suppliciter Te rogantes a

malis," which yields the same 'tri, pro, de'-set, except for the minor change in the sixth syllable from ad to

a (as underlined above)—cf. (F-Pn lat. 7211, f. 100r, in Santosuosso 1991; Henderson 1969, 24).

According to the survey provided in Dolores Pesce's edition, that is the only manuscript that presents the

Trinitas protege text and setting (Pesce 1999, 547). A presentation about these and other syllable-sets (both

Guidonian and non-Guidonian) is given in the work by Henderson (1969, 17–36)—cf. also (Smits van

Waesberghe 1953, 98–105; Oesch 1954, 63–70).

12

implementation of the setting of the "Trinum et unum" text and its correspondent syllables,

nor even of the proposition of a full system of seven hexachordal deductions as shown in

FIG . 1 .1 (Medieval System or Recta-Gamut, post-Guido d'Arezzo).29 In his Musica

practica, Ramos de Pareja (1482, pt. 1, tr. 1, ch. 7, ff. b3r–v; Wolf 1901, 18–19; [trans.]

Miller 1993, 63–65) also mentions both sets of solmization syllables, crediting only the 'ut,

re, mi'-set to Guido d'Arezzo, while indicating no source or author for the 'tri, pro,

de'-set—but implying that both sets were still in use during his time.30

(ii) Musica ficta versus Musica recta

Since the syllables were not attached to any specific step-letter (or any fixed-pitch),

they could be sung on any step-letter within the system, and not only on those shown in

FIG . 1 .1 . To be sure, that figure is a representation of the gamut of musica vera (true

music) or musica recta (right, rightful, proper, conscientious, virtuous, straightforward,

correct music), whereas theoretically the gamut of musica falsa (false music) or musica ficta

29 The copy of the Epistola contained in F-Pn lat. 7211 seems to be the only one to include a

diagram of hexachordal deductions similar to the one presented in FIG. 1 . 1 . The diagram, however, shows

syllables drawn from the 'tri, pro, de'-set, and the deductions are made over the span from Γ to dd (or, from

G to d", in modern pitch-equivalents), thus the last hexachord starting on g (i.e., g') is left incomplete—cf.

(F-Pn lat. 7211, f. 100r, in Santosuosso 1991; Henderson 1969, 25; Pesce 1999, 27n, 547).

30 Cf. assessments by Palisca (NG 1, 7: 807; NG 2e, §2 (v), s.v. 'Guido of Arezzo') and by

Henderson (1969, 31–33).

13

(feigned, imagined, invented, fictitious music) comprises everything that does not fit into that

strict pattern.

Following the usage of most modern scholarship, the opposing pair of qualifying

terms 'ficta' and 'recta' will be adopted throughout the present work. In medieval and

Renaissance musical theory, however, there was a handful of terms being used instead of

today's common musica ficta and its near antonym musica recta. The medieval term

musica falsa, for which musica ficta came to substitute in modern scholarship, was often

opposed to musica vera .31 Some theorists, especially but not exclusively medieval (and

apparently not the majority among them), tended to use both musica recta and musica vera

as synonyms, or at least with closely related meanings, although there seem to have been

more authors who reserved the adjective recta for discussions of mensural notation.32 A

substitution for falsa (though it was not the only qualification in use) began to occur

(tentatively) only in the later part of the thirteenth century. The adoption of the term ficta

not only was not shared by all authors thereafter, but the abandonment of the term falsa

31 Karol Berger, in his Musica ficta (1987), shows an exception to the above mentioned tendency

in modern scholarship, for he has preferred to use the terms 'ficta' and 'vera' as a more appropriate opposing

pair. His choice is perhaps also more accurate with regard to the early uses of the term ficta, for when it

came as a replacement for falsa, the term vera was kept as its opposite—seemingly, there was no immediate

conceptual need for change regarding this latter term.

32 Some medieval authors (especially those from the thirteenth century) also used the term falsa

in order to explain the 'inappropriate' mensural interpretation of middle notes in ligatures—cf. Franco de

Colonia, Ars cantus mensurabilis, ca. 1250 (F-Pn lat. 16663, f. 79r; GB-Ob 842, ff. 53v; GS 3: 7; CS 1:

124; Reaney and Gilles 1974, 45), or more frequently to describe the 'inappropriate' use of imperfection in

various circumstances (in reference to plicae, or to alterations, or to longae, etc.)—cf. Magister Lambertus,

Tractatus de musica, ca. 1260's/1270's (I-Sc L.V. 30, f. 25v; CS 1: 271), Anonymous St Emmeram, De

expositione musicae, ca. 1279 (Sowa 1930, 17, 24, 49, 113; Yudkin 1990, 93, 104, 145, 254).

14

gained force only in the Renaissance. The following quotations will provide a brief account

of how musica ficta and related terms were defined, in this case from the mid-thirteenth

century to the early-sixteenth century. Notice, particularly, that in the second quotation,

from the anonymous St. Emmeram author—writing around 1279—falsa is employed as a

primary term, but always paired with ficta, as an alternative synonym.

Falsa musica est, quando de tono facimus

semitonium, et e converso.

(Garlandia med. 13th cent.; CS 1, 166)

False music is when out of a tone we make

a semitone, or vice versa.

(my translation)

————————

Si quaeratur, quid sit falsa musica sive ficta,

dicimus, quod falsa musica est variatio

vocum necessaria de tono in semitonium vel

e converso per falsam mutationem sive

fictam. Alii sic describunt: falsa musica est

illud, quod est imponibile * in aliquo

propassu, et fit <in> cantu organico ad

melodiam faciendam.

(St. Emmeram ca. 1279; Yudkin 1990, 274;

Sowa 1930, 124)

If it is asked what false or contrived [ficta]

music is, we say that false music is the

necessary variation of notes from a tone to a

semitone or the reverse by a false or

contrived [ficta] mutation. Others describe it

thus: False music is that which can be

imposed in a certain situation, and it occurs

in organal melody to make a musical sound.

(Yudkin 1990, 275)

* Sowa gives the word "impossibile" instead of "imponibile"[interpolations mine]

————————

Falsa musica est quae non potest inveniri in

Gamma manus secundum artem plani

cantus [...]. Vel sic: Falsa musica est

adventicia scientia inventa causa adiutorii.

(Petrus palma ociosa 1336; Wolf 1913–14,

513)

False music is that which cannot be found

in the Gamut of the hand, according to the

art of plainchant [...]. Or else: False music

is the adventitious science [i.e., unusual, or

extraneous knowledge or skill] devised for

the sake of help.

(my translation)

————————

15

[F]icta musica est vocum fictio, sive vocum

positio in loco ubi esse non videntur,

sicilicet ponere mi ubi non est mi, et fa ubi

non est fa, et sic ulterius. De qua ficta

musica est primo sciendum quod ipsa

nunquam ponenda est nisi loco necessitatis,

eo quod nihil ponendum est in arte

sine necessitate.

(Prosdocimus 1412, tr. 3, ch. 1; CS 3: 198;

Herlinger 1984, 70, 72)

Musica ficta is the feigning of syllables or

the placement of syllables in a location

where they do not seem to be--to apply mi

where there is no mi and fa where there is no

fa, and so forth. Concerning musica ficta, it

is necessary to know first of all that it is

never to be applied except where necessary,

because in art nothing is to be applied

without necessity.

(Herlinger 1984, 71, 73)

————————

Conjuncta est dum fit de tono regulari

semitonium irregulare aut de semitonio

regulari tonus irregularis, vel sic:

Conjuncta est appositio b rotundi aut

quadri in loco irregulari.

[...]

Ficta musica est cantus propter

regularem manus traditionem aeditus.

(Tinctoris 1495, ff. a iiiiv, [a viii]r; CS 4:

180, 184; Machabey 1951, 12–13, 28;

Parrish 1963, 14, 32)

Coniuncta is when an irregular semitone

is made out of a regular tone, or an irregular

tone out of a regular semitone, or else:

Coniuncta is the apposition of

b-rotundum or -quadrum in an irregular

place.

[...]

Musica ficta is song that has been

produced as a result of the regular tradition

of the hand.

(my translation; cf. Parrish 1963, 15, 33)

————————

De vocibus fictis seu musica ficta

Caput Decimum,

Quid est musica ficta? Quae per voces fictas

modulatur. Quae dicuntur voces fictae? Quae

canuntur in aliqua claue, in qua essentialiter

non continentur, nec etiam in eius octaua: vt

si fa canatur in alamire vel elami.

(Cochlaeus 1511–14, tr. 2, ch. 10, f. C ir)

On ficta-syllables or musica ficta

— Chapter 10.

What is musica ficta? It is that which is

sung through ficta-syllables [voces fictas,

literally, feigned voices]. Which [of those]

are named ficta-syllables? Those that are

sung on any step-letter [clavis, literally,

clef] in which they are not essentially

contained, nor even in their octave: as

when fa is sung in a-la-mi -re or e-la-mi .

(my translation; cf. Miller 1970, 46)

Thus, from the thirteenth to the sixteenth centuries, authors usually agreed in

16

defining musica ficta as step-occurrences that could not be found in any place within the

established medieval system (the 'hand'). In other words, musica ficta was virtually a

parallel system of steps that was forged and effected outside the standard gamut. Those

steps, then, were extra manum occurrences.33 This term can be rendered in at least five

different translations: 'outside the hand,' 'in addition to the hand,' 'free from [the measure of]

the hand,' 'without the hand,' or 'beyond the hand.' Each of these translations for 'extra

manum,' however, imply different concepts that, ultimately, may affect the understanding of

both practice and theory associated with musica ficta. 'Extra manum' may be used to

represent all those steps that are external to the hand (in modern terminology, any of the

pitches from f" and above, or from F and below), as well as all those that may lie in

between the regular steps represented in the hand (i.e., any of the pitches that are modernly

called accidentals—except for b and b '). It might also refer to any of the modern pitches

presented in FIG . 1 .1 , provided they were not solmized with any of the regular step-syllables

(i.e., not solmized with recta-syllables). If a step on the letter D was solmized with the

syllable ut (D-ut), it would constitute a step not to be found within the hand (i.e., a ficta-step,

or extra-manum step), for the only syllables available on a recta-D are sol and re—thus,

33 The 'hand,' or more properly called the 'Guidonian hand,' apparently served as a mnemonic

device for solmization, by being a representation of the gamut (i.e., of the post-Guidonian system—see

FIG. 1 . 1 ). In that capacity, all twenty-two steps of the gamut were placed on twenty different places ('loci')

of the left hand, occupying the pads of palm and fingers. Each place (locus) was assigned for one single

step, except for the double-steps that occupied single loci: -fa/ -mi occupied the locus on the tip of the

minimum, and -fa/ -mi occupied the locus on the lower pad of the annular—in those double-step loci, as

shall be seen in the following chapters, the context of the melody was enough to provide a decision on

which step should be chosen for solmization. See Berger's "The Hand and the Art of Memory" (1981).

17

D-sol and D-re are recta-steps. Extra-manum steps are always included in a

ficta-hexachord, which should always maintain the same intervallic structure (configuration)

as the other recta-hexachords. Also, the very existence of an extra-manum step

presupposes some intervallic relation with a preexisting step-letter within the recta-gamut.

Thus, extra manum should really be understood in the sense of 'sprung from the hand.'

As for the term musica falsa (alternately, falsa musica), Johannes de Garlandia

(fl. ca. 1240) may have been one of the first theorists to have explicitly assumed, used, and

defined this adjectival construction as a representation for that set of extra-manum steps,

while justifying the need for their use.34 In his case, the term accounts for a practice of

34 There is another explicit use of the term musica falsa recorded in the treatise Summa musice.

Christopher Page defends that this treatise was written ca. 1200 by two authors, identified as Perseus and

Petrus, who presented musica falsa as an alternative term for musica irregularis—which the authors appear

to have considered the primary term. (The value-word 'vitium'—i.e., 'vice,' translated below as "fault"—is

also presented as a complementary qualifier, which helps to establish a liberal-arts context to the discussion,

since that word is related to the disciplines of the trivium, especially dialectic and rhetoric.)

Et assimilatur hoc vitium propositioni falsae, quae a dialectico multum vitatur. Musica irregularis

et talis iure musica falsa vocatur, et multum vitetur. Item in formatione cantus novi non apponitur

inutiliter repetitio intervalli eiusdem [...].

(Perseus and Petrus ca. 1200, cap. 23; GS 3: 238; Page 1991, 199)

This kind of fault may be compared to a false proposition of the kind which is rigorously avoided

by the dialectitian. Such irregular music is rightly called musica falsa and it should be

scrupulously avoided.

(Page 1991, 122)

Differing from the tendency which Garlandia represents in his time, the authors of this treatise

consider musica falsa as something to be avoided, unnecessary, and unjustifiable. Page's date for the treatise

is however debatable, especially if one considers the several quotations from Aristotle's works contained in

the treatise. Aristotle's writings were still in the process of early dissemination in 1200 meeting great

resistance on the part of the Church. That resistance would recede, eventually allowing Aristotle's ideas

into Christian theology, only after the works of St. Thomas Aquinas (1226–1274) became accepted.

18

deliberate step change (i.e., from tone to semitone, and vice versa) within a realm whose

existence was assumed in practice (i.e., extra manum steps), but was not completely

validated or accepted in earlier theory. The theoretical validation of falsa musica granted the

adjective 'falsa' a force of a substantive, i.e., transformed the qualifier into agent, or (in

Aristotelian terms) allowed the 'accident' to be transformed into 'substance.' In that

substantival capacity, the term 'falsa' could now be perceived as an active determinant of the

quality of music, which could not be accepted and therefore needed to be challenged, based

on moral, theological, and correlated philosophical grounds. Also, the validation by musical

theory (in the application of the concept of falsa musica to measured music or to

plainchant) was further enhanced by the introduction of other rhetorically and

philosophically acceptable terms, for example: vitium (vice), corruptio (corruption),

coniuncta (conjunct), irregularis (irregular), inusitata (out of the ordinary), and others.

It is necessary to keep in mind that historical discussions and attempts to define the

procedure now called musica ficta frequently evoked dualities of the kind vice-virtue,

falsity-truth, fiction-reality, etc., that conveyed a myriad of moral and social connotations,

and were intended to enhance the proper understanding and use of the concepts being

defined. Earlier authors (mostly before the twelfth century), for example, tended to be more

ambivalent in their definitions, and generally identified the practice of musica ficta as a

series of 'musical deviations' effected either deliberately or haphazardly, or because of

custom or ignorance—in other words, arguing that those were as 'errors' from which the

music should be summarily cleansed in order to obtain a correct version. Some tentative

19

terminological standards can be identified in those early texts, but the profusion of terms

indicates the desire to provide a better understanding by amplification of meaning (i.e., by

employing synonymia) within discussions infused with both rhetorical and philosophical

contents, excerpted below. (Underlines have been added to facilitate visualization of the

key-terms referring to the practice of musica ficta, and its related theoretical concepts.)

In maximum saepe errorem vulgares cantores

labuntur, quia vim toni et semitonii,

aliarumque consontiarum minime

perpendunt. Id enim unusquisque eorum

eligit, quod primum auribus placuerit, vel

quod facilius ad discendum pronuntiandumve

provenerit: fitque magnus error in multis

cantibus, cuius modi sint. [...]. Illos itaque

cantores si de aliquo cantu interrogaveris,

cuius modi sit, illico respondent, quod

nesciunt, ac si perfecte congoscerent. Quodsi

ab eis argumentum, unde hoc sciant,

quaesieris, titubantes dicunt: quia sit similis

in principio et in fine aliis cantibus eiusdem

modi; cum de nullo omnino cantu, cuius

modi sit, sapiant, nescientes, quod unius

vocis dissimilitudo modum mutare

compellat, ut haec antiphona: O beatum

pontificem! quae cum in principio et fine

secundi modi esset, propter illius tantum

vocis elevationem, ubi dicitur: o Martine

dulcedo. in primo tono a Domno Oddone

curiosissime est emendata. Itemque in

antiphona: Domine qui operati sunt haec

diligentius probare poteris: nam si eam

incipias in sexto modo, ut multi probant, in

F. littera, non discrepabit ab eo modo, usque

ad semitonium, quod est in tabernaculo tuo,

in una syllaba. Sed quia in usu ita est, et

bene sonat, emendari non debet. Sed

inquiramus, an forsitan in alio tono incipia-

Mediocre singers often fall into the greatest

error because they scarcely consider the

qualities of tone and semitone and of the

other consonances. Each of them chooses

what first pleases his ear or appears easiest

to learn and to perform, so that a

considerable error is made with respect to

mode of many chants. [...]. These singers,

if you question them about the mode of any

chant, promptly reply with what they do not

know as though they knew it perfectly. But

if you ask them how they know it, they say

falteringly: "Because at the beginning and

end it is like other chants of the same

mode," although they do not know the mode

of any melody. They do not know that a

dissimilarity in a single pitch forces the

mode to change, as in the antiphon O

beatum Pontificem, which, although in the

second mode at the beginning and end, was

most painstakingly emended to the first

mode by Dom Odo, merely because of the

ascending interval on which are sung the

words O Martine dulcedo. You can examine

this more thoroughly in the antiphon

Domine qui operati sunt, for if you begin, as

many attempt to, on F, in the sixth mode, it

will not depart from that mode until the

semitone, at in tabernaculo tuo, on one

syllable. Yet since it is thus in use, and

sounds well, it ought not to be emended.

20

tur, totaque in eo modo consona inveniatur,

eamque emendari opus non sit. Incipe itaque

eam in G. littera, hoc est, in octavo modo,

et regulariter in eo stare probabis.

(Ps.-Odo ex. 10th cent. D; GS 1: 256; PL

133: 763–764)

But let us inquire whether it might not begin

in another mode, in which all will be found

consonant and in which there will be no need

for emendation. Begin it, then, on G, that is,

in the eighth mode, and you will find that it

stands regularly in that mode.

(SR 1998, 205–206; cf. SR 1950, 110–111)

————————

Dissonantia quoque per falsitatem ita in

canendo subrepit, cum aut de bene dimensis

vocibus parum quid demunt gravantes, vel

adiiciunt intendentes, quod pravae voces

hominum faciunt; aut cum ad praedictam

rationem plus iusto intendentes vel

remittentes, neumam cuiuslibet modi aut in

alium modum pervertimus, aut in loco qui

vocem non recipit, inchoamus.

Quod ut exemplo pateat, in

Communione Diffusa est gratia, multi

propterea, quod erat incipiendum in .F. uno

tono deponunt cum ante .F. tonus non sit;

sicque fit ut finis Communionis eiusdem

ibidem veniat ubi nulla vox est. Cantoris

itaque peritiae esse debet quo loco vel modo

quamlibet neumam incipiat, ut ei vel si

motione opus est, affines voces inquirat.

Hos autem modos vel tropos graece

nominamus protum, deuterum, tritum,

tetrardum.

(Guido d'Arezzo ca.1026–28; Smits van

Waesberghe 1955, 134–138; B-Br II 784, ff.

8v–9r; GS 2: 10–11; PL 141: 389–390)

False notes also creep in through

inaccuracy in singing; sometimes performers

deviate from well-tuned notes, lowering or

raising them slightly, as is done by untrue

human voices. Also by ascending or

descending more than is right for the

prescribed interval, we pervert a neume of a

certain mode into another mode or we begin

at a place [in the scale] which does not admit

[that] note.

To make this clear by an example, take

the communion Diffusa est gratia. Many

put propterea, which should begin on F, a

whole tone down, although there is not a

whole tone just below F. As a result the

end of this communion comes where there is

no note. The place and mode where each

neume begins should be left to the

judgement of the singer, so that if it needs to

be transposed [si motione opus est], he may

search out related [affines] notes. These

modes or tropes we name, from the Greek,

protus, deuterus, tritus, and tetrardus.

(Babb 1978, 66)

[Interpolations in the original translation]

————————

Principales chordae dicuntur quae in

troporum dispositionibus principatum

sortiuntur, sicut in autento proto principales

The principal strings [i.e., steps] are named

among the first [ones] that are assigned in

the disposition of tropes [i.e., protus,

21

sunt istae: prima finalium, prima

superiorum, prima excellentium. Finalis est

merito principalis inprimis: quia, si

secundum convenientiam, quam ipsa

praedocet, cantum incipimus et usque ad

finem procedere non possumus, ostendit

illum esse aut vitiosum, aut iuxta alium

modum gubernandum. Quidam cantant

illam antiphonam Alliga domine in vinculis

secundum tercium tonum, secundum finalis

convenientiam incipientes eam in G., sed

quia defectus occurrit chordarum ut cantari

non possit, cogitemus eam aut secundum

alium modum iubilandam, aut penitus esse

mendosam. Sed falsam esse dicere prius non

debemus, quam secundum omnium finalum

convenientiam incipientes exploremus, si in

ullo modorum inoffensam reperiamus eam;

sicut istam iuxta primi finalis

convenientiam inchoantes in F. sine

scandalo percantabimus.

(Aribo ca. 1070's; Smits van Waesberghe

1951b, 13–14; GS 2: 203; PL 150:

1313–1314)

deuterus, tritus, and tetrardus], just as in the

authentic protus the principal ones are these:

first of the finales [d], first superiores [a],

first of the excellentes [d']. The finalis is, in

the first place, deservedly the principal

[step]: because, if according to convenience,

which teaches itself in advance, we begin the

chant and we cannot proceed all the way to

the end, it exhibits that [chant] to be either

vitiated, or prone to controlling another

mode. Certain people sing that antiphon

Alliga domine in vinculis according to the

third tone [i.e., mode], beginning it on G [g ]

according to the convenience of the finalis

[i.e., e]. But because a defect of the strings

[i.e., steps] occurs where it cannot be sung,

we consider it [i.e., the antiphon] either [to

be a] rejoicing according to another mode, or

to be internally erroneous. But we should

not say [it] rather to be false, than we

[should] explore the beginnings according to

the convenience of the finales, if in any of

the modes we find it unimpaired. In the

same way we shall sing through that

[antiphon], without scandal, starting on F

[f], close to the convenience of the first

finalis [d].

(my translation)

————————

Cum enim in usualibus neumis intervalla

discerni non valeant, cantusque, qui per eas

discuntur, stabili memoriae commendari

nequeant, ideoque in cantibus plurimae

falsitates subrepant. Hae autem omnia

intervalla distincte demonstrent, usque adeo,

ut et errorem penitus excludant, et

oblivionem canendi, si semel perfecte sint

cognitae, non admittant: [...].

Since in the ordinary neumes the intervals

cannot be ascertained, and the chants that are

learned from them cannot be securely

committed to memory, many inaccuracies

creep into them. These Guidonian neumes,

on the other hand, indicate all the intervals

unambiguously. Not only do they

completely obviate error, but, once learned

perfectly, they will not allow one to forget

how to chant from them. [...].

22

Sed et in communione Beatus servus

levis error habetur, qui per unum podatum

incongrue prolatum efficitur. Hunc autem

quidam sic corrigunt, quod Dominus a trite

diezeugmenon in mese cadere faciunt, et

invenerit in parhypate meson incipiunt et

super omnia in lichanos meson; alii autem

ita emendant quod invenerit iuxta usum

incipiunt, et penultimam eius in mese

inchoantes in lichanos meson emittunt, et

ultimam in hypate meson, incipientes in

parhypate meson exire faciunt, super omnia

secundum priores corrigunt. Mihi autem

facilior correctio videtur, si ultima syllaba

invenerit in lichanos meson per unisonum

cantetur, quod et Guarino et Stephano in

musica subtilibus placet.

Sed si quis obiiciat deesse in quibusdam

locis semitonia, dicimus non esse ibi

necessaria semitonia, ubi ipsi videtur. Saepe

etenim ex cantorum ineptia evenit, quod

inter alias cantuum depravationes

semitonia proferunt ubi proferre non debent,

et interdum negligunt ubi negligere non

debent.

(Johannes Affligemensis ca. 1100, ch. 14;

Smits van Waesberghe 1950, 133, 137–138;

GS 2: 257, 258; PL 150: 1422, 1423)

In the communion Beatus servus too an

error is easily made by performing a single

podatus unsuitably. Some correct it thus:

they make Dominus fall from the trite

diezeugmenon [c] to the mese [a], and they

begin invenerit on the parhypate meson [F]

and super omnia on the lichanos meson [G].

Others so emend it that they begin invenerit

as is the custom, but after beginning its

penult on the mese [a] they end it on the

lichanos meson [G]. Beginning its final

syllable on the hypate meson [E], they make

it end on the parhypate meson [F]. Then

they correct super omnia in the same way as

do the former. Yet to me it seems an easier

correction if the last syllable of invenerit is

sung to a unison on the lichanos meson [G],

as pleases Guarinus and Stephanus, who are

musically discriminating.

If anyone protests that semitones are

missing at certain points, we rejoin that

semitones may not be necessary where it

seems to him that they are. Singers from

ineptitude often make, among other

corruptions of the chant, semitones where

they should not be made and now and then

omit them where they should not be

omitted.

(Babb 1978, 147, 148–149)

[Ellipsis mine; interpolated pitch-letters in the original translation]

In FIG . 1 .4 , below, based on the Worcester antiphonary from the thirteenth century,

notice that the antiphon Domine qui operati sunt begins on c, and presents the -rotundum

at taber-na-culo (a rightful step-letter in Pseudo-Odo's system)—the wavy-tailed notes

represent plicae. If the non-emended version (as Pseudo-Odo described) did begin on F,

then, at taber-na-culo, it should produce an E a tone lower than F, creating an extraneous

23

step within Pseudo-Odo's system.35 According to Pseudo-Odo, such a step would be an

inconceivable 'error' produced by 'mediocre' ("vulgares"), or 'faltering' ("titubantes")

singers. However, if Dominie qui operati sunt was made to begin on G (as Pseudo-Odo

proposed), the second note for the syllable -na- would be placed on an F (a step rightfully

found within the system).

ÚÄÄÄ¿ÚÄÄÄ¿ ÚÄÄÄ¿ÚÄÄÄ¿

ÚÄÄÄ¿ ÚÄÄÄ¿ ÚÄÄÄ¿ ÚÄÄÄ¿ ÚÄÄÄ¿

8 Do-mi -ne qui o -pe -ra -ti sunt ju –

8 sti-ti – am, ha – – bi-ta-bunt in ta-ber – na – cu-lo tu – – o,

FIGURE 1 . 4 - "Domine qui operati sunt"—according to the version given in the

thirteenth-century Worcester antiphonary (GB-WO F. 160;

Mocquereau 1922, 2: 395).

In FIG . 1 .5 , below, the surviving version of the antiphon Alliga Domine in vinculis

(from the Antiphonale monasticum) is in agreement with Aribo's suggested correction. The

35 Further explanations concerning Domine qui operati sunt are given by Strunk (SR 1950,

111–112) and James McKinnon (SR 1998, 206). In these works, the reproduction of the Worcester version

places the b-rotundum immediately before the two-note ligature of taber-na-culo, whereas in the original

that sign was placed before the syllable in, as shown in FIG. 1 . 4 . The function of this pre-positioning of

the b-rotundum (as will be seen in a later chapter) is to enforce the solmization of a particular hexachord (in

this case, the -hexachord) beginning already at the first syllables of the phrase in tabernaculo tuo—the

previous hexachords were: the -hexachord on the word Domine, the -hexachord, from qui operati to

habitabunt. Since these changes from one hexachord to another might entail the singer to take a breath, the

earlier positioning of the b-rotundum will prevent an unwanted (and unnecessary) breath in the middle of the

word tabernaculo. (The whole process of solmization, from the deduction and grouping of hexachords, to

how and where to change from one to another, will be explained in the following chapters.)

24

defectus (defect) of which he speaks would be found in an indirect tritone outlined on the

word "na-ti-o-nes," if the antiphon was truly sung according to the third mode, with an

initial note beginning on g.

AI g 25 Ant. ÚÄÄÄÄ¿

|

*

ÚÄÄÄÄ¿ÚÄÄÄÄ¿

ÚÄÄÄÄ¿ |

ÚÄÄÄÄ¿ ÚÄÄÄÄ¿

ÚÄÄÄÄ¿ÚÄÄÄÄ¿

! ÚÄÄÄÄ¿

!

8 L - li - ga Do -mi - ne in vin -cu – lis

8 na - ti - o - nes gen -ti – um, et re – ges e - a – rum

8 in com – pe - di – bus. E u o u a e FIGURE 1 . 5 - "Alliga domine in vinculis"—according to the version given in

the Antiphonale monasticum (1934, 911).

In Aribo's correction, he suggested a change to the first mode, in order to avoid the tritone,

and (in accordance with that) a change to f as the first note—the presence of b s (in fact,

-fas) does not really affect the mode, as they are necessary not only to avoid tritones, but

also to avoid hexachordal mutation (as shall be seen in chapters to follow). Both changes

were certainly necessary, for if there was just a change to the first mode, and the initial note

was maintained on g, then all es in FIG . 1 .5 would have to be changed to f s (on the

syllables: nati-o-nes gen-ti-um, et re-ges earum in com-pedibus). These, of course, find no

correspondent steps in the standard medieval gamut, and would then constitute further

25

instances of what Aribo might have qualified as "vitiated," "erroneous," "false," or

"impaired," or even another kind of "defect" or "falseness." No doubt these qualifications

are just alternative designations for what today may be called musica ficta, though Aribo (at

least in this case) does not recognize them as necessary nor as justifiable occurrences.

In the communion Beatus servus, mentioned in the text by Johannes Affligemensis,

the deviations from the theoretical system were even more pervasive than he seems to have

attested (see FIG . 1 .6 , below). By invoking the 'inaccuracies,' 'errors,' the tendency for

'corruption' of chants, and 'omissions' (i.e., 'negligence') on the part of 'inept' singers,

Affligemensis condemns the alterations improperly imposed on the chant by means of

unjustifiable habits, and proposes another, simpler way to avoid deviations. Further, he

asserts that some of those habits might lead to inappropriate placement of semitones where

they are really not needed. The alterations shown in FIG . 1 .6 might seem excessive,

considering that at the end (as in the beginning), the interval between F and G is made to

follow the regular whole-tone paradigm, even if it had been an unusual semitone for most of

the chant. (The version given in this example reproduces Charles Atkinson's own

reconstruction of the chant—slurs indicate ligatures, a wavy glissando-like sign indicates a

quilisma [cf. vene-rit, beginning of the second staff], and modern accidental signs are

applied directly to individual notes).36

36 In Babb's translation (1978, 148–149), the different versions of Beatus servus, which are

reconstructed according to the detailed descriptions by Johannes Affligemensis, show only one deviation on

the last syllable of invenerit (f -g )—in the same way as shown in FIG. 1 . 6 . In Atkinson's interpretation

(1988), the use of the musica ficta in this chant is established as an enactment of 'vices of language,'

especially with regard to 'barbarisms' and 'solecisms' (following the descriptions given in the anonymous

26

8 Be – a – tus ser – – – – – – vus quem cum

8 ve – – ne-rit do – mi-nus in-ve-ne – – rit vi -gi – lan – tem.

8 A – men di – co vo – bis su -per om -ni a bo - na

8 su -a cons-ti – – tu -et e – – – um.

FIGURE 1 . 6 - "Beatus servus"—according to the reconstructed version conceived

by Charles Atkinson (1988, 195).

It may be construed, from those four quotations above, that earlier authors (here

represented by Pseudo-Odo, Guido d'Arezzo, Aribo, and Johannes Affligemensis—

ex. 10th cent. to in. 12th cent.) did not always approve of musica ficta and its necessity.

From a brief interpretation of the contexts, however, some nuances of understanding may be

revealed about how far these earlier authors took their disapproval or acceptance of musica

ficta. Some, like Pseudo-Odo and Aribo, seem to have been more willing to condone those

'deviations,' based on effectiveness of previous practice, even if they advised against it and

Scolica enchiriadis). In Atkinson's modern reconstruction (not a transcription), the inclusion of signs

between the notes of those two-note ligatures is highly unlikely (cf. invene-rit vi-gi-lan-tem … di-co

vo-bis), and is nowhere to be found in the sources.

27

eventually took the time to propose 'emendations.' Of the two, Aribo's discourse seems to

be more condescending, for while he makes use of strong words such as "vitiosum"

("vitiated" or "vicious") and "defectus" ("defect"), he also lightens their weight by stating

that one should seek to understand nuances and consider ("explorare," i.e., "explore")

corrections without uproar or blemish ("sine scandalo," i.e., "without scandal"), and even

considers that one should not be hasty in attributing 'falseness' to music without seeking

those alternative nuances. Pseudo-Odo's statements are less lenient, for while he seems

more flexible than Aribo with regard to chants that do not conform to systematic theoretical

standards, his attitude derives from futility, from the declared impossibility of altering

long-established practices, especially since the practical (acoustical) results seem at least

acceptable. In any case, Pseudo-Odo does not abstain from qualifying as "mediocre"

("vulgares," i.e., "vulgar") those "faltering" ("titubantes") performers who run astray from

the safe ground of theory, due to mispreparation or even choice. Guido, however, seems to

have been completely against the use of such "false notes," although he also admitted that

such occurrences were, unfortunately, common in his day. As Guido's statements made

clear (not only in the quotation above but throughout the Micrologus), he was very much

critical of those performers who, with their "untrue voices" ("pravae voces"), "deviate"

(from "demere"), "pervert" (from "pervertere"), or "subvert" the chant (the latter as implied

by the verb "subrepere," although Babb's translation does not emphasize this sense). Like

Guido, Johannes Affligemensis was unwilling to accept deviations from the theoretical

standards, and is even less willing to condone nuances, which he takes the time to analyze in

28

order to prove that they are responsible for the "many falsities [that] subvert the chant"

(loosely interpreted from "in cantibus plurimae falsitatis subrepant").37 Finally, one must

notice that all of the four quotations deal with plainchant, whose repertory would usually be

kept within the limits of the theoretical medieval system of steps. Even so, all of those

authors admit that practice frequently crossed over and beyond those limits, integrating the

realm of musica ficta into plainchant—even if they criticized its practice.

For the purposes of this dissertation, since the gamut (shown in FIG . 1 .1) was the

representation of the realm of musica recta, and since the realm of musica ficta was

everything that did not fit within that system, they will be referred to, respectively, as

recta-gamut and ficta-gamut (even though the extension of such an imaginary ficta-gamut

varies from author to author, and from epoch to epoch). As mentioned briefly in the

commentary about the term extra manum (above), within the Guidonian tradition, ficta-steps

were represented (or obtained) in one of three ways: (a) by applying new syllables (ranging

from ut to la) to any set of places (i.e., to virtually any diatonicum group of six contiguous

step-letters) within the previously established recta-gamut (in other words, creating new

steps by changing the syllable of preexisting steps to new syllables); (b) by conceiving new

steps between the preexisting steps of the recta-gamut; (c) by conceiving new steps, in new

loci, outside the gamut. In any of these cases, the new ficta-steps always bear some relation

37 This aspect of resistance against (or reluctant acceptance of) ficta-occurrences may be used to

support Christopher Page's date of the Summa musice: ca. 1200, for its authors may have been writing

very much within the same tradition that runs from Pseudo-Odo, Guido, Aribo, and J. Affligemensis—a

tradition which seems to have survived, virtually unbroken, until the early thirteenth century.

29

to preexisting steps (modifying, appending, adding), and necessarily establishing new

hexachords (ficta-hexachords). In the first case, for example, E-la-mi (e), a-la-mi-re (a),

and -fa (b ) were all part of the recta-gamut, while E-sol (e), a-sol (a), and -ut (b ) were

all steps on a ficta-gamut, and pertained to ficta-hexachords. In the second case, one could

conceive of steps such as C-mi (c ), B-fa (B ), E-fa (e ), all part of the ficta-gamut. In the

third case, as seen earlier, any steps including ff-fa (f") and above, or FF-mi (F ) and below,

were steps said to pertain to the ficta-gamut—even if some of those could find

correspondent steps in other octaves of the recta-gamut. It is necessary to remember,

especially with regard to the latter case, that the recta-gamut contained only seven

hexachords, having no hexachord beginning on FF (which would account for a FF-ut) or on

c-sol-fa superacuta (which could account for a ff-fa).38 Notice that ficta- and recta-steps

are not limited to step-letters: each step ought to be considered with its whole designation

(letter-plus-syllable), i.e., a step ought to be considered within its own hexachordal

context.39 Thus, the actual sound (pitch) of a given step is not important in determining

whether or not it pertains to the ficta-gamut, but whether its designation can or cannot be

found among those established for the recta-gamut. For example, -fa (representative of the

trite synemmenon, and equivalent to the modern b ) is always a recta-step, but the same

sound can be understood as a ficta-step if it is solmized as -ut, or -sol, etc. It should be

38 As time went on, however, some theorists proposed the integration, in the recta-gamut, of

some ficta-steps, specifically those matching the designation of a recta-step in another octave—cf. note 41.

39 These considerations, about the understanding of a step within its own hexachordal context,

will become clearer in subsequent chapters.

30

noted also that in the medieval recta-gamut the 'b rotundum' or 'b molle' (whose sign is )

occurred only in the higher places—i.e., in those regions denominated acutae or

superacutae. In other words, three different s (gravis, acuta, superacuta) were included

in the recta-gamut (and considered recta-steps, provided they were solmized with the

syllable mi), but only -fa (b ) and -fa (b ') were considered recta-steps; B-fa grave (B )

was considered a ficta-step.40

Nonetheless, a few authors seemed to disagree with this understanding, particularly

as indicated by their attempts to propose expansions to the existing recta-gamut. On the

one hand, toward the beginning of the sixteenth century some writers defended the

interpretation that if a step has a correspondent in any octave of the recta-gamut, then it may

as well be considered a regular recta-step—e.g., B (B-fa grave), or even f" (ff-fa), a

position encountered in the works of Adam de Fulda (ca. 1445–1505), Johannes Cochlaeus

(1479–1552), and Stefano Vanneo (ca. 1493–p. 1539), among others.41 On the other hand,

40 My use of letters framed by an underline and an overline, particular to this dissertation, is here

used for the representation of module of a pitch-letter (similar to what would be the module of a number in

the mathematical sense). Whenever such a symbol appears, no octave is determined, and if it appears as a

designation to a hexachord (e.g., -hexachord), it will stand for its initial letter (the letter that takes 'ut' as

its solmization-syllable).

41 Adam de Fulda, mentioning that one can regularly find steps both below Γ or above ee at least

as early as Du Fay, includes in his treatise a diagram showing both an F below Γ (in this dissertation

designated as FF, equivalent to the modern F) which he names "hyperexiapathon" , and ff above ee (also ff

in this dissertation, equivalent to modern f"), which he names "origneboleon"—cf. (Adam de Fulda 1490,

ch. 8–9; GS 3: 350–351). Cochlaeus, in his Tetrachordum musices, implies that a B-fa (B ) may be an

acceptable recta-step, since the syllable fa is indeed found in other octaves of the step-letter B—cf.

(Cochlaeus 1511–14, tr. 2, ch. 10, ff. C i; [trans.] Miller 1970, 46), whose first paragraph has been quoted

earlier in this chapter. Stephano Vanneo goes even further, and includes one full octave below the standard

gamut (i.e., starting on a G, equivalent to G'), and another full octave above (i.e., expanding to a step

31

since the standard gamut did not include a low B-fa (modern B ), there were also a few

medieval authors who preferred to disavow even b and b ' ( -fa and -fa) of their place

within the recta-gamut, because of this lack of a correspondent octave among the lower

notes.

In hoc litterarum ordine non computatur B

rotundum: patet enim omnibus quod non sit

aliqua de gravibus, cum etiam inter eas

nusquam ponatur. Sed nec aliqua est de

acutis, cum nulli gravium per duplarem

coniungatur proportionem. Est autem

inventum non ad proprietatem finalium

determinandam, sed ad servandam in

plerisque cantibus euphoniam, quam apud

eos minueret vel auferret tritonus qui apud B

quadratum terminatur.

(Anon. Tr. Cist. ca. 1147; Guentner 1974,

27–28)

In this order of the letters, B-rotundum is not

included. In fact, it is evident to everyone

that it is not any of the graves, since it is

indeed nowhere placed among them. But

neither is it any of the acutae, since it is

united to none of the graves by means of a

proportion dupla. On the other hand, it has

been invented not for the purpose of

determining the propriety of the finales, but

for the purpose of preserving euphony on the

majority of the chants, as far as among them

it might lessen or remove the tritone, which

is framed by the B-quadratum.

(my translation; cf. Guentner 1974, 47)

equivalent to e''')—(Vanneo 1533, bk. 1, ch. 10, ff. 10r–11v). Vanneo also presents an illustration of the

back of the hand, in which the new G (i.e., G') is considered to be the new "Gammaut," and is assigned to a

position just above the wrist, whereas the other steps are assigned to the knuckles. Karol Berger presents a

brief discussion on this tendency toward expanding the recta-gamut, including some relevant quotations or

references to these and other late fifteenth-century and early sixteenth-century theorists—(K.Berger 1987,

13–16). He also states that "Ciconia in his Nova musica […] considers B [i.e., B ] to be part of the

regular gamut" (K.Berger 1987, 16). It is true that Ciconia presents at least two diagrams of the monochord

in which he includes a b-rotundum between low A and low B, but his statements are somewhat

contradictory—cf. (Ciconia ca. 1400, bk. 1, chs. 16–18; Ellsworth 1993, 76–85). In chapter 16 ("De

litteris monocordi"—"On the letters of the monochord"), Ciconia provides a very brief presentation (two

short paragraphs and one diagram of the monochord) of a gamut that goes only from Γ to D superacuta

(according to his terminology in this chapter). Ciconia also ascertains the inclusion of this B equivalent

by stating that "[t]he authors of music notated twenty-two letters in the monochord" ("[v]iginti et duas

litteras auctores musice in monocordo exaraverunt")—cf. (Ciconia ca. 1400, bk. 1, ch. 16; Ellsworth 1993,

76, 77). Shortly after, using a different terminology in chapter 19 ("De divisionibus monocordi"—"On the

divisions of the monochord") , he states that "b synemmenon does not have a tone, a diapente, and a

diapason below itself" ("b synemmenon sub se tonum et diapente et diapason non habet")—cf. (Ciconia

ca. 1400, bk. 1, ch. 19; Ellsworth 1993, 84, 85).

32

This statement, by the anonymous author (or authors) of the Tractatus Cantum

quem Cisterciensis ordinis ecclesiae consueverant., is found within a description of the

modes, and denotes a contemporaneous resistance to the idea of modal transposition. The

author (or authors, of this and other treatises within the same tradition) appear to have

considered the reintegration of -rotunda (at least the usual higher ones) into the system

only in the presence of extreme, unavoidable melodic situations (like an upcoming tritone).

Otherwise, those -rotunda were considered virtually extraneous steps that could as well

fall into the ficta category, at least within the line of thought followed in this

mid twelfth-century treatise. Wherever a ficta-step was needed—according to either

tradition—the music would have to provide convenient enough indications (explicit or not),

for the performer to deduce it, based on knowledge and experience.

In order to indicate any such unusual (or 'fictitious') hexachordal-syllable

assignments, the scribe or the composer would provide the score with the so-called

ficta-signs: for fa, and for mi (at least as far as explicit indications are concerned). Of

course, there are graphic variants to them (these vary by personal choice on the part of the

scribe, or according to the notational tradition each one followed), but their basic shape can

generally be recognized without difficulty in music notation, and their respective

descriptions as b-rotundum (or molle) and b-quadratum (or durum) hardly change in the

majority of historical theoretical discussions. Two other signs, however, might appear as

indications for the hexachordal syllable mi, instead of the usual : and . These latter

mi-signs seem to have appeared only after the beginning of the fourteenth century, or

33

perhaps shortly before the third decade of the century. These signs (or at least ) may in

fact have originated within the propositions and definitions of Marchettus da Padova with

regard to musica ficta (or rather generically termed musica colorata, as he preferred) and

his own division of the whole tone into five equal parts.42 Thus, at least based on

Marchettus's treatises, the signs and were meant to indicate a specific division of the

whole tone, which would not yield to the same interval with the surrounding steps as the

42 According to Marchettus's description in the Pomerium (1318/19, bk. 1, pt. 1, tr. 4., ch. 4),

the sign for square b should be differentiated from another sign which he idiosyncratically named falsa

musica. The former should take the shape (also describe in the Lucidarium, 1317/18, tr. 8, ch. 1), and the

latter should take the shape —describe as having an upward stem on its right and a downward stem on its

left. Marchettus's falsa musica sign (which he seems to have originally devised) served his unique

propositions for dividing the tone into five equal parts—it should be employed to divide the whole tone into

a diesis and a chromaticum semitone (the latter, in his terminology, was equivalent to four dieses). When

employed in accordance with Marchettus's proposition, the falsa musica sign would be indicating a

chromaticum semitone above the note to which it is applied—i.e., interpreting in a modern context, the

sign would serve as an indication that the 'pitch' should be raised chromatically by four of Marchettus's

dieses—cf. Marchettus's Lucidarium (Marchettus 1317/18, tr. 2, chs. 6–8, and tr. 8, ch. 1; [ed. and trans.]

Herlinger 1985, 140–157, 270–281; [ed.] GS 3: 73–75, 89), and also his Pomerium (Marchettus 1318/19,

bk. 1, pt. 1, tr. 4; [ed.] Vecchi 1961, 68–74; [ed.] GS 3: 134–136; [trans.] Renner 1980, 52–60). (For the

sake of reference, notice that Gerbert [GS 3: 89] designates the relevant section in tractatus octavus of

Marchettus's Lucidarium as chapter 2, while Herlinger gives it as chapter 1.) Despite the description given

by Marchettus, in the editions of Pomerium available to this date (GS 3: 136; Vecchi 1961, 73–74), the

sign is graphically presented as (Gerbert), and as (Vecchi)—cf. (Renner 1980, 59), for a translation

according to Vecchi's edition. In Herlinger' s edition of the Lucidarium, he used the fourteenth-century

manuscript I-Ma D.5 inferiore as the main and most reliable source, which also included a copy of the

Pomerium—Herlinger (1985, 23–24) speculates that the copy of this manuscript (apparently the earliest)

may even have been overlooked by Marchettus. This manuscript is the only one that presents musical

examples with a consistent differentiation between the square b and falsa musica signs, "precisely as

Marchettus prescribed" (Herlinger 1985, 27). Of the eighteen manuscripts consulted by Herlinger, only

three make a clear graphic distinction between the two signs, but in most manuscripts (whose dates range

from the early fourteenth to the early sixteenth century), signs such as , , , , # or were used

indistinctively for both square b and the falsa musica sign, sometimes even two signs in the same

manuscript were used with no the distinction regarding their function within Marchettus's propositions—cf.

(Herlinger 1985, 21–62).

34

sign for b-quadratum ( ). Despite these differences, and while the sign does not appear

to have been truly adopted, the sign seems to have gained currency from the early Ars

Nova through the Renaissance, as an indication for the hexachordal syllable mi, and as a

rightful substitute for —virtually no differentiation was made between the latter two in

terms of musical practice.43 In any case, it seems only natural that signs would have been

used or omitted in accordance with regional determinations of the limits of one gamut or the

other, as well as the predilection (regional or personal) for one shape or the other. Now,

since it is the position of the semitone (mi-fa) that indicates the hexachord to be read, these

signs were more than enough to specify or represent the whole hexachord. For instance, if

the semitone is placed between b and c', the syllables of the -hexachord will apply; if the

semitone falls between a and b , then the syllables of the -hexachord will apply.

Therefore, in solmization, a great emphasis was placed on the identification of the semitone,

and the signs that framed the hexachordal semitone (i.e., the signs for mi and fa) were used

in order to clarify that position within a melodic gesture. In other words, solmization

depended on identifying (with a good degree of certainty) where the semitone lies within a

melodic gesture. When the position of that internal semitone was easily recognizable, there

would be no need to indicate it by means of a sign for mi or fa (i.e., by means of one of the

43 For further and very informative commentaries on the use and possible chronology of all of

the signs, see the unparalleled survey provided in Karol Berger's Musica ficta (1987, 17–29). Also, it must

be noted that in some sixteenth-century original publications (especially of Germanic origin), and

occasionally in earlier manuscripts, the -quadratum can take the form , or else resemble the shape of a

brevis with very short stems going up and down on both sides, and in some cases it may even be confused

with the modern natural-sign ( ), but these are likely due to particular calligraphic choices or scribal

idiosyncrasies.

35

ficta-signs). A sign was however necessary (either for a recta- or for a ficta-step) when the

position of the semitone was unclear (or ambiguous), or when it had to be changed within

the course of a musical work, or else when its place was unusual with regard to the prevalent

gamut. The latter case applied only to ficta-steps, while the two former cases could involve

either recta-steps or ficta-steps.

Sunt enim duo signa falsae musicae, scilicet,

molle et quadratum. Ubi ponitur

rotundum dicitur fa; ubi vero quadrum

dicetur mi. Et sic potest unam speciem in

aliam transmutari, ut visum est in capitulo

de proportionibus.

(Anon. 2 ?ex. 13th cent.; CS 1: 312; Seay

1978, 32)

Indeed, two are the signs of false music [i.e.,

ficta-signs], namely, -molle et -quadratum.

Where -rotundum is placed, [the syllable] fa

is said; however, where -quadrum [is

placed], [the syllable] mi will be said. And

thus one species [of interval] can be

transmuted into another, as it was seen in

the chapter on proportions [of intervals].

(my translation; cf. Seay 1978, 33)

Here, "to be transmuted" (from "transmutari") refers to a generic process of change

from a tone into a semitone—or vice versa—in much the same way as the term musica falsa

was described in the mid-thirteenth-century treatise by Johannes de Garlandia, quoted

above.44 In the recta-gamut, b and bb were the only places where two different varieties of

steps were available ( -fa / -mi and -fa / -mi), necessary since two different varieties of

intervallic configurations surrounded those places: if there was a semitone below and a tone

above, the step should be solmized fa, but if there was a tone below and a semitone above, it

should be solmized mi. Thus, these were also the only places that could serve as

representations of such a radical 'change' and their correspondent signs (round-b and

44 Later in this dissertation, the term 'transmutation' will be employed in another, more specific

meaning—cf. chapter 6 .

36

square-b) were a natural choice for use as ficta-signs. Another aspect of the relevance and

emphasis placed on the semitone lies in the fact that theorists (and practitioners) were

prompted to its identification, since it was considered a difficult interval both in singing, as

well as in calculating its exact ratio (i.e., both in practice and in speculative music).

Namque semitonium ipsum magis

artificiosum et ipsa proportione atque prolatu

natura et arte difficilius est tono.

(Gaffurius 1496, bk. 1, ch. 3, f. a iiijv)

For indeed, the semitone, itself more

artificial and by its own proportion, is more

difficult than the whole tone, [as it is]

revealed by nature and by art.

(my translation; cf. Miller 1968, 30;

Young 1969, 21)

To be sure, the concept of musica ficta (and therefore the identification of

ficta-steps) is as much dependent on the establishment of the medieval gamut (i.e., on that

specific collection of steps) as it is dependent on solmization. Now, although solmization

need not follow the Guidonian paradigm, most of the same procedures and concepts used in

the Guidonian hexachordal solmization are also applicable to other kinds of solmization, at

least during the medieval and Renaissance periods, even before Guidonian solmization

became the norm. The dependence (even if only partial) of musica ficta on proper

solmization, led to the incorporation of many of the basic procedures of solmization into

writings about musica ficta. For example, 'change' became the underlying pivotal concept

that permeated both, whether understood as a 'modification' from tone into semitone (and

vice versa), or as a 'shift' between two different hexachords.

In the following chapters of this dissertation, solmization procedures will be

explained mainly through the Guidonian paradigm and a systematization proposed in order

to explain how musica ficta was practiced and conceived. The conceptual relations between

37

solmization and musica ficta (and supplementary understandings of their processes) will be

illuminated by references to some particular figures of rhetoric. It will also become evident

that musica ficta (as a feature of 'solmization' in its generic sense, that is, as a process of

reading notated music, whether or not it followed hexachordal parameters) was a practice

that not only can be applied to polyphony (usually the context in which modern scholarship

has formulated its guidelines toward ficta), but to monophony as well.

38

— CHAPTER 2 —

PRINCIPLES OF HEXACHORDAL SOLMIZATION

(i) Deduction of Hexachords

The deduction of the Guidonian hexachord consisted in applying the solmization

syllables ut, re, mi, fa, sol, la to any sequence of six consecutive steps that conform to the

structure T-T-S-T-T, thus providing the mi-fa interval as the only internal semitone.

Deductio est vocum de uno loco ad alium per

aliquam proprietatem ordinatam ductio.

[…]

Proprietas est propria quaedam vocum

deducendarum qualitas.

(Tinctoris 1495; CS 4: 181, 186; Parrish

1963, 18, 50)

Deductio is the conduction of voices (i.e.,

syllables) from one place to another through

some ordered proprietas (i.e., 'propriety').

[…]

Proprietas (i.e., propriety) is a certain quality

proper of deduced voices.

(my translation; cf. Parrish 1963, 19, 51)

According to these assertions by Johannes Tinctoris (in his Terminorum musicae

diffinitorium), the deduction (i.e., deductio) is a process through which one realizes, or finds

(either in performance or in theory) a hexachord, by applying the syllables used in

solmization to adjacent steps (or places)—this is the meaning implied in the phrase "de uno

loco ad alium," translated above as "from one place to another." The qualification 'adjacent'

is, of course, not explicit in Tinctoris's text, but there is basically no other way to find and

conduct an "ordered proprietas" (i.e., an intervallic structure, or order). In the generic

39

sense, "proprietas" is itself a term that stands for any intervallic structure, but in the context

of Tinctoris's work, it is the one structure within the Guidonian hexachordal tradition that

determines seven hexachords within the gamut, and that makes use of the correspondent

sequence of six solmization syllables. In the particular sense, "proprietas" suggests the

necessity for qualification of specific regions within the gamut, where the sequence of

syllables will contain one or the other variety of b (one may thus conceive of the 'molle

proprietas' for all those hexachords that contain a -molle, and of the 'durum proprietas ' for

those hexachords that contain the -durum), or else regions where no variety of b is found

(the 'natura' or 'naturalis proprietas'). "Deductio," in its turn, stands not only for a process

of finding hexachords, but of finding a defined, particular hexachord—for the objective of

the process of finding (deducing) is to determine and choose one hexachord at a time. In

fact, Tinctoris's definitions show a broad enough scope to invite generalizations, for in the

entries given above he does not mention a particular 'order' of syllables (or pattern), only

that there is one common to all unities, and he also does not state if they are hexachords,

tetrachords, heptachords, or some other number of 'places'; he suggests, however, that

unities can be grouped according to "proprietas" (i.e., according to 'certain proper

qualities').45 Notwithstanding the broadness of the above definitions, other passages in

45 This interpretation of terms is indebted to the work of Carl Parrish, one of the first scholars to

translate Tinctoris's Terminorum musicae diffinitorium (1495) in its entirety, and the first to provide an

English translation—the only previous translation was one in French done by Armand Machabey, and

published in 1951. Parrish, however, chose to translate and understand 'proprietas' simply as 'hexachord,'

and also declared that there existed a synonymical relation between 'deductio' and 'hexachord,' in the context

of Tinctoris's works. In a footnote (quoted below) referring to the entry on 'Deductio,' Parrish explained

some of the nuances he conceived for his translation. (cont. ...)

40

Tinctoris's work may attest to the fact that he was referring to 'unity' and 'order' within the

Guidonian tradition (i.e., the Guidonian hexachord and its particular intervallic structure).

A la mi re acutum est linea cujus clavis est

A, et in qua tres voces scilicet la, mi et re

canuntur: la per naturam ex loco C fa ut; mi

per b molle ex loco F fa ut gravi; et re per b

durum ex loco G sol re ut gravi.

[...]

Manus est brevis et utilis doctrina ostendens

compendiose qualitates vocum musicae.

(Tinctoris 1495; CS 4: 178, 185; Parrish

1963, 6, 40)

A-la-mi-re acutum is the line of which clef

is A, and in which three voices (i.e.,

syllables) are sung, namely la, mi , and re: la

through natura (i.e., via naturalis proprietas)

according to the place C-fa-ut; mi through

b-molle (i.e., via molle proprietas) according

to the place F-fa-ut gravis; and re through

b-durum (i.e., via durum proprietas)

according to the place G-sol-re-ut gravis.

[...]

The hand is a brief and useful doctrine (i.e.,

method) that abbreviatedly reveals the

qualities of the musical voices (i.e., the

syllables).

(my translation; cf. Parrish 1963, 7, 41)

The two entries above (for manus and for the step a-la-mi-re), given in Tinctoris's

The word deductio is one not often found in early treatises, and seems to be used by Tinctoris as a

sort of synonym for "hexachord," a word which he never uses [...]. In place of it, he employs

three other terms, each with a slightly different meaning: 1) proprietas, 2) b durum (also b molle

and natura [...]), and 3) deductio. The distinction appears to be as follows:

1) proprietas is the name for the particular arrangement of intervals in any

hexachord, regardless of its position in the gamut;

2) b durum, b molle, and natura are those beginning on g, f, and c respectively,

regardless of the octave range in which each occurs;

3) deductio is one particular hexachord in a particular range.

In his treatise on the hexachord system, Expositio manus (Coussemaker IV, p. 8), Tinctoris says

that there are seven deductions: those on G, c, f, g, c', f', and g'. A somewhat similar use of the

word deductio is found in the anonymous treatise, Quatuor principalia, c. 1380, formerly attributed

to Simon Tunstede (Coussemaker IV, p. 219).

(Parrish 1963, 83; ellipses mine)

There should be no doubt that Tinctoris used these terms in the sense interpreted by Parrish, even

though his wording may obscure the relation between the terms and prevent the expansion of meanings to

include the ideas of 'process' (in the case of 'deductio') and 'intervallic structure' (in the case of 'proprietas').

41

Terminorum musicae diffinitorium, are signs of a definite compliance to the Guidonian

tradition. Other particular signs that his theoretical thought was based on the Guidonian

hexachordal solmization are found in the definitions for the other steps within the

recta-gamut, which are given at their appropriate alphabetical position in that encyclopedic

work. Tinctoris is not the only one to have used the terms deductio and proprietas in the

sense and context given above, for one can find other assertions regarding these concepts,

both before his time and in contemporaneous literature.

Notandum est quod iste proprietates

predicte debent ordinari, secundum quod, in

deductionibus artis manus sinistre, voces

et claves appropriantur hoc modo: Gamma ut

in regula vel in linea habet unam clavem et

unam vocem. G est clavis, ut est vox.

Cantatur per quadrum et ad semetipsum

descendit.

A re in spatio habet unam clavem et

unam vocem; a est clavis et, re est vox.

Cantatur per quadrum et descendit ad ut de

gamma ut.

mi in linea habet unam clavem et

unam vocem; b est clavis, mi est vox.

Cantatur per quadrum ad ut de gamma ut.

C fa ut, in spatio habet unam clavem et

duas voces; C est clavis, fa et ut sunt due

voces; fa cantatur per quadrum ad ut de

gamma ut; ut cantatur per naturam, et ad

semetipsum descendit.

(Garlandia p. 1240; CS 1: 159)

It must be noted that these above

mentioned proprieties are the ordinary

ones, according to which, in the art of

deductions of the left hand, step-syllables

and step-letters (voces et claves—lit., voices

and clefs) are appropriated (i.e., made proper)

in this fashion: Gamma-ut, [placed] on the

ruler or on the line [of the staff], has one

step-letter and one step-syllable. G is the

letter, ut is the syllable. It is sung through

-quadrum and descends to itself.

A-re, in the space, has one step-letter

and one syllable; a is the letter, and re is the

syllable. It is sung through -quadrum and

descends to ut of gamma-ut.

-mi, in the line, has one step-letter and

one syllable; b is the letter, mi is the

syllable. It is sung through -quadrum [and

descends] to ut of gamma-ut.

C-fa-ut, in the space, has one step-letter

and two step-syllables; C is the letter, fa and

ut are the two syllables. Fa is sung through

-quadrum to ut of gamma-ut; ut is sung

through natura, and descends to itself.

(my translation)

The above quotation, from Johannes de Garlandia's Introductio musice, shows one

42

of the first statements that used the terms deductio and proprietas with the same meaning as

the one disclosed in Tinctoris's works, and pointing to the same kind of practice and

context. In Garlandia's sentences singing 'through -quadrum ' means making use of a

hexachord that belongs within the durum proprietas (for only such a hexachord would

contain that particular variety of b), and singing 'through natura' means making use of a

hexachord that belongs within the naturalis proprietas (for only such a hexachord would

contain no variety of b). The indication 'descends to itself' denotes that those particular

steps, namely Γ-ut and C-ut, are the starting and returning points of the hexachords to which

they belong. Another quotation that pertains to the same tradition of concepts is given by

the anonymous treatise of Franconian tradition entitled Tractatus de discantu.

Nota quod quando dicit continet duas voces,

vel tres, vel quatuor, debes intelligere

seriatim prolatus, sicut sunt in deductionede ut, re, mi, fa, sol, la.

(Anon. 2 ex. 13th c.; CS 1: 309; Seay

1978, 22)

Notice that when it is said [that] it [a step]

contains two syllables (voces), or three, or

four, you ought to understand the

arrangement step by step, as in the

deductio of ut, re, mi , fa, sol, la.

(my translation; cf. Seay 1978, 23)

In addition to these accounts of related meanings of the terms deductio and

proprietas (and the practical use associated with them), one finds other references to them

as early as the mid-thirteenth century, and they seem to disappear by the end of the fifteenth

century.46 This apparently limited time-frame for actual assertions regarding those terms,

validating their meaning and use according to what has been exposed above, should not

46 Several other references regarding the term deductio are given the Lexicon musicum Latinum

medii aevi (LmL, 6: 784–786). All of them are confined to the time-frame given above: mid-thirteenth

century to end of the fifteenth century.

43

preclude their contextualized application in the present discussion, since other time periods

sharing in the same Guidonian tradition also utilized the same concepts, although these

particular terms may not have been used systematically, nor with such a clarity as in other

periods. Thus, the terms proprietas and deductio will be hereby used with the following

meanings: proprietas as a quality shared by hexachords; and deductio as a process of

finding hexachords, but not as a hexachord in itself.

Within the gamut (FIG . 1 .1), Guidonian tradition established three basic types of

hexachord, described according to the variety of b they contained (or its absence): (a) a

durum (hard) hexachord was any hexachord containing the durum variety of b (i.e., a

b-quadratum); (b) a naturale (natural) hexachord was any hexachord containing no variety

of b; and (c) a molle (soft) hexachord was any hexachord containing the molle variety of b

(i.e., a b-rotundum). This kind of description, proper to historical treatises, emphasizes the

place where one (who wishes to solmize) needs to look in order to locate the semitone

within the hexachord (i.e., the position of the syllables mi and fa), since the identification of

the semitone was essential for solmization—as discussed in chapter 1. In modern musical

pedagogy, however, there is a tendency to organize and study scales and their pitches.

Accordingly, it seems appropriate to have a description of hexachords based on their first

steps (those which would bear the syllable ut); thus, the designations for those three basic

types of hexachord can be as follows: -hexachord, -hexachord, and -hexachord, which

may also be called recta-hexachords.

44

Now, ficta-hexachords are also determined by the position of the syllables mi and fa,

but none of their steps are found in the regular gamut (i.e., the recta-gamut)—i.e., they are

all classified as ficta-steps, despite the fact that there are sound-equivalences between some

recta-steps and ficta-steps. In the case of -hexachords, all steps (except -mis) have

sound-equivalents in the recta-gamut—given a -hexachord starting on the step-letter D:

the pitches d, e, g, a, b are respectively equivalent both to the ficta-steps D-ut, E-re, G-fa,

a-sol, -la, and to the recta-steps D-sol-re, E-la-mi, G-sol-re-ut, a-la-mi-re, -mi; while f is

the equivalent to the ficta-step F-mi, and f is the equivalent to the recta-step F-fa-ut. A

similar case applies to -hexachords, for which all steps (except -fas) have

sound-equivalents in the recta-gamut—given a -hexachord starting on the step-letter :

the pitches b , c', d', f', g' are respectively equivalent both to the ficta-steps -ut, c-re, d-mi,

f-sol, g-la, and to the recta-steps -fa, c-sol-fa-ut, d-la-sol-re, f-fa-ut, g-sol-re-ut; while e is

the equivalent to the ficta-step e-fa, and e is the equivalent to the recta-step e-la-mi. These

ficta-hexachords ( -hexachords and -hexachords) are the only ones in which all of their

steps (except one) have sound-equivalents in the recta-gamut. Notice that this

correspondence between ficta-steps and recta-steps may be established only via their actual

sound (they are, in modern terms, pitch-equivalents). There are three main points to be

summarized here: (a) all steps in a ficta-hexachord are denominated ficta-steps, whether or

not they have sound-(pitch)-equivalents in the recta-gamut; (b) not all ficta-steps are

necessarily equivalent to modern accidental inflections (for the classification of ficta-steps

depends on particular letter-plus-syllable designations that are not found in recta-steps, and

45

not in their actual sound); and (c) in the deduction of an entire ficta-hexachord, it is enough

to find only one syllable in a step where it is not regularly found in the recta-gamut (the

other ficta-steps are deduced or implied accordingly, as long as their solmization can be

effectively kept within the limits of that ficta-hexachord).

In all instances, the determination (or deductio) of any hexachord (recta as well as

ficta ones) may be expressed by a syllable associated with a step-letter; or in other words,

any step (with the appropriate letter-plus-syllable designation) would serve as a determinant

of a particular hexachord. For example, any durum or -hexachord is expressed by saying

ut on any , re on any , mi on any , and so on, up to la on any , and similarly the

naturale or -hexachord is expressed by saying ut on any , up to la on any , as well as

any molle or -hexachord is expressed by saying ut on any , up to la on any . Notice

that the solmization of any one of those syllables would be enough to express the

solmization according to one sole hexachord, for in any given step-letter (or pitch) one given

syllable can pertain to only one hexachord. Medieval and Renaissance musicians may have

certainly faced the problem of how to indicate a syllable within the score, allowing for the

performer to solmize the appropriate hexachord intended by the composer, and which would

be the most functional syllable to be indicated. To solve this problem, in concordance with

the emphasis placed on the semitone, it would seem reasonable and sufficient to indicate the

semitone itself, by means of signs that would either denote the syllable mi or the syllable fa.

For example, if a sign indicating the solmization syllable mi (represented by a sign based on

the b-durum, in the shape of either , , or the like) is placed before any one , it will

46

indicate that the hexachord whose solmization is being effected is the -hexachord, for it is

the only hexachord where a is solmized mi—in modern terminology, those s are

equivalent to 'non-inflected s'. Likewise, if a sign indicating the solmization syllable fa

(represented by a sign based on the b-rotundum, via the shape , or the like) is placed on the

space or line of any one , it will mean that the hexachord being effected at that moment is

the -hexachord, in which case the on that line or space is to be solmized fas, and will

necessarily establish a semitone with the step below—in modern terminology, these -fas

are equivalent to 'accidentally inflected s'. Although the above explanation sounds

obvious, it is very important to stress that the primary function of those signs (either

mi-signs or fa-signs: generically called ficta-signs) is to indicate a solmization syllable

(not necessarily a modern accidental inflection), thus properly indicating the hexachord to

be solmized.47

Historical treatises were also careful to group hexachords according to the varieties

of b they contained—i.e., according to their proprietas. Among the three basic types of

hexachord, those that contained the b-durum variety (the -hexachords) were said to have a

durum proprietas (or hard quality); those that contained no b variety (the -hexachords)

were said to have a naturale proprietas (or natural quality); and those that contained the

b-molle variety (the -hexachords) were said to have a molle proprietas (or soft quality).

These groups could be expanded into families that not only included the three basic types of

47 The conceptual differences between 'ficta-signs,' 'accidentals,' and other possible terms will be

discussed in chapter 8 (ii) and (iii).

47

recta-hexachords, but included ficta-hexachords as well. The durum family may be defined

in two ways: (a) it consists of all hexachords whose deduction is usually effected through

the indication of a mi-sign ( , or , or ); or (b) it consists of all hexachords that contain the

step-letter b-quadratum (equivalent to ) in any octave of the gamut—e.g., -hexachords,

-hexachords, -hexachords, etc. Similarly, the molle family may be thus defined: (a) it

consists of all hexachords whose deduction is generally effected through the indication of a

fa-sign ( ); or (b) it consists of all hexachords that contain the step-letter b-rotundum

(equivalent to ) in any octave of the gamut—e.g., -hexachords, -hexachords,

-hexachords, etc.48 It might be noted that the two definitions for each of those families

(durum and molle) mean virtually the same thing (they are simply two different approaches

used for explaining the same proprietas). Any hexachord indicated by means of one of

those signs (either for mi or fa) will necessarily include among its step-letters one of the

corresponding varieties of b (either b-durum or b-molle, respectively); conversely, when

there is a need to indicate the semitone (of a hexachord whose step-letters include some

variety of b), the choice of indication will necessarily fall on the mi-sign (if the hexachord

includes a b-durum) or on the fa-sign (if the hexachord includes a b-molle). The naturale

48 Regarding the expansion of the medieval system of steps and hexachords, some limits to each

family may already be envisioned. On the molle-family side, a limit for hexachordal expansion may be

found before the -hexachord is reached (and any other hexachords beyond), for it would yield to -fa-mi,

which is a virtual impossibility. On the durum-family side, a -hexachord (and beyond) is also a virtual

impossibility, for it would yield to a -mi-fa. These steps are not only difficult (though not impossible) to

explain theoretically (by means of hexachordal deductions, or other paradigms available to medieval and

Renaissance theory), but also an adequate notation (indication) for them would be feasible only in very

particular situations—one of those is found in Adrian Willaert's Quid non ebrietas—cf. (Levitan 1938–39;

Lowinsky, 1956; Bent 2002, 22–25, 106–111, 125–129, 204–206).

48

family, which comprises only hexachords that include no variety of b, is said to consist only

of one type of hexachord: -hexachords. There are only two such hexachords in the

recta-gamut (one starting on C-fa-ut, the other starting on c-sol-fa-ut), but there may be

other ficta-hexachords of this type (starting on C-letter places other than the ones belonging

to the recta-gamut). Recta -hexachords do not make use of any sign to indicate their

semitone, but ficta -hexachords (being outside of the gamut) do need signs in order to be

deduced: a common case in medieval and Renaissance notation is the use of a fa-sign ( ) on

the place of the step-letter ff, thus producing the ficta-step ff-fa (equivalent to f '), which

implies the existence and solmization of a ficta -hexachord starting on cc-ut (a step whose

sound is the same as the recta-step cc-sol-fa). In any of these cases, note that a sign does

not function as an indication of a single tone. Since it indicates a syllable (which exists only

within the context of a hexachord), the sign ultimately functions as an indication for an

entire hexachord. Regarding the definitions given above for the durum and molle families,

one exception may be found in reference to recta - and -hexachords: they may be

indicated by an actual sign only when the choices for solmization become unclear or

doubtful. When the melodic context clearly implies the solmization of one of these

hexachords, those signs are unnecessary—thus, definition (a) in both cases (for the durum

and molle families) is more fitting to ficta-hexachords of each family than to recta ones.

The recognition and solmization of hexachords is, as suggested above, not dependent solely

on the indication of ficta-signs, but also on a proper inspection of the melodic context.

Concerning recta-hexachords of any type, it may be said that a melodic gesture is generally

49

sufficient to imply the solmization of one of them. In the recognition and consequent

solmization of ficta-hexachords, however, two factors must be always taken into account: the

melodic gesture, and the ficta-signs that might be present (including an appropriate

interpretation of those signs, according to their position, relatively to ligaturae, syllabic

divisions of the text, tempora, clefs, phrases, etc.).

(ii) Stages of Solmization

Before entering into discussions about the recognition of hexachords (whose first

factor, the 'melodic gesture,' will be undertaken in section [iii]), it may prove informative to

read a late-fifteenth-century report on how solmization practice was taught, carried out, and

which levels of knowledge and skill were being recognized or ideally expected. Based on

that report (from Gaffurius's Practica musice), it appears that both practical and speculative

musicians (from performers to composers, scribes, and even theorists) were schooled in the

same kind of basic music-reading: solmization based on hexachordal structures. It also

seems that the expected stages involved in basic music-training in Gaffurius's time were not

so different from those expected in modern times. In a first stage, musicians started by

solmizing each note (or in the modern practice solfeging); then in the next stage they went

on to vocalizing the notes, and finally in the third stage (seemingly after a higher level of

comprehension had been reached) they should be able to read their part with full attention to

all its texts (musical and literary).

50

Tribus insuper modis voces quas notulae

declarant pronuntiari solent. Primo modo

solfizando idest syllabas ac nomina vocum

exprimendo scilicet vt re mi fa sol la: vt hic.

Moreover, the voces [steps], which the notes

[figures in staff notation] indicate, are

usually pronounced in three ways. The first

way is by solmizing, i.e. by articulating

syllables and names of sounds, namely ut,

re, mi , fa, sol, la: as here.

! ! | || vt re mi fa sol la Quem quidem pronuntiationis modum

tanquam legem initiandis pueris

praeaponendam tradunt.

As a rule to be preferred, they teach such a

way of pronouncing them [i.e., the notes] to

initiating boys.

Secundo modo: sonos ac voces tantum

emittendo ommissis penitus litteris ac

syllabis et dictionibus: quod exercitatus

cantor facile prosequitur hoc modo.

The second way: by uttering only sounds and

steps made thoroughly void of literature

[i.e., text], and of syllables and articulations

[i.e., phonemes]; which a trained singer is

able to follow easily, in this way.

||

Tertio modo: quascumque dictiones vt

antiphonas et reponsoria: et ipsarum verba

cantilenarum notulis ipsis subscripta

pronunciando: Ad quem tanquam ad finem

ellecti modulaminis clerici deducuntur. vt

hic.

The third way: by pronouncing any

articulations and the exact words,

underscoring their correspondent notes of

songs, as in antiphons and responsories.

According to such [a way], selected members

of the clergy are led to the end of a chant.

Salue rex glo ri e chri ste

| || | | | | | | | |

(Gaffurius 1496, bk. 1, ch.3, ff. a iiijv–vr) (my translation; cf. Miller 1968, 30–31;

Young 1969, 21–22)

There is no doubt that these three stages differ with regard to sight-reading skills,

and that each one is a prerequisite for the next. These stages might refer not only to the

51

schooling process, but also might extend to the qualification level of different musicians

(i.e., whether a well-trained musician would be able to learn a new part without having to

resort to a process of sight-reading that included the two first stages, going directly to the

third stage). Now, the last sentence in the quotation above can also be read with a slightly

different meaning: "According to such [a way], members of the clergy are led to the end of a

selected chant." If the first translation ("selected members of the clergy are led to end of

[any kind of] a chant") is accepted, it would imply some social discrimination (i.e., virtually

equivalent to 'the chosen ones') within a class (the clergy, the oratores) that, by nature, is

already differentiated and perhaps even privileged with regard to other social casts, and

would also imply that once the last stage of training had been reached, the musician could

perform anything (or nearly that) at a first reading. If the alternative, second translation

("[any] members of the clergy are to the end of a selected chant") is favored, it could mean

that the third stage of part-reading is dependent on previous selection of the musical work

itself—it is likely that this selected chant (to be read according to the precepts of that third

stage) was not too elaborate or too complex (otherwise there would be no need for

selection). From the alternative translation, one also could infer that there are chants (those

that were not selected) which cannot be implemented through a third-stage sight-reading

without having to resort to the first two stages (or perhaps at least to one of them), since

they are probably too elaborate or complex. In any case, both translations appear to imply

that the third stage was not always reached, either because there was a limit (whether by

means of arbitration or by natural selection) to the actual number of accomplished

52

musicians able to deftly handle such a level, or because the complexity of the music did not

allow for random pieces to be sung with all their musical and literary nuances at first sight

(perhaps not even after a first reading).

Gaffurius is historically classified among humanistically oriented theorists who

undertook the interpretation of (and eventually used) classical models as a means to support

and promulgate their own aesthetic ideas, but who were not necessarily concerned with

accurately reporting on the current stage of musical knowledge or practice. In the above

quotation, however, the text seems very clear with regard to where the description ends, and

where Gaffurius's expectations (or comments) begin. The expectations are present not in

the training stages (first: basic; second: intermediate; third: advanced), but in the social

groups implied by Gaffurius's allegorical representation (first: the illiterate people; second:

the learned; third: the selected).49

In Gaffurius's description, this kind of hexachordal solmization is clearly used for

the vocal repertoire, but one can hardly deny that the instrumental repertoire would have

made use of solmization (and of musica ficta), though it remains to be investigated which

49 In his Musica Ficta, Karol Berger quoted the same passage from Gaffurius's Practica musice,

and provided additional references to three later sources containing descriptions of three similar stages (or

levels) of solmization: Cochlaeus's Tetrachordum musices (1511–14, tr. 2, ch. 6, ff. B iiiir–v); Lanfranco's

Scintille di musica (1533, 16); and Vanneo's Recanetum de musica aurea (1533, bk. 1, ch. 13,

ff. 12r–v)—cf. (K.Berger 1987, 7, 193n). Earlier, at the outset of his first chapter, Berger also quoted a

passage from Adrian Petit Coclico's Compendium musices (1552, ff. B ijr–iijr) containing another, similar

description—cf. (K.Berger 1987, 2, 189n). In all of these descriptions, there are implicit social references

that demand acknowledgement, and which may enlighten how solmization and musica ficta was effected

with regard to different social groups—or (at least in Gaffurius's case) which social groups were expected to

actually go through all the stages and thus achieve a higher level of knowledge.

53

kind of solmization that would be, and on what level. In the quotation given below, from the

Tetrachordum musices (1511–14), Johannes Cochlaeus presents three kinds of

music-reading that are apparently similar to Gaffurius's division. These kinds, however, are

not restricted to the concept of progressive, mutually exclusive stages as in Gaffurius's, but

rather determine distinct ways of execution by different groups of performers. (Cochlaeus's

characterization is, therefore, not exclusively dependent on the concept that each group

represents different skills and levels of knowledge—as in Gaffurius's socially charged

description, although his presentation is not devoid of allegorical references to social

groupings.) In his description, Cochlaeus seems to suggest the following meanings: the

first and second kinds of reading are applied to vocal music, and the third to instrumental

music. The first kind is accomplished by solmizing one's part—i.e., singing by means of

the solmization syllables (very much the same way as Gaffurius's first stage). The second

kind deals with singing the parts already with their full text—i.e., by means of the syllables

given in the poetic text (thus similar to Gaffurius's third stage). In Gaffurius's assertions

the first two kinds appear to constitute mutually exclusive stages: one in which performers

who had achieved a higher level of skill would be expected to read parts with their full text,

and another in which performers were expected to use solmization with syllables. In

Cochlaeus's assertions (quoted below from his Tetrachordum musices), however, the two

kinds appear to indicate procedures that should be executed consecutively, despite one's

skill or level of study. Perhaps both should happen in reading elaborate or complex music

(as suggested in one of the interpretations above for Gaffurius's assertions).

54

Triplex modulandi forma [in margin]

Contingit tamen tripliciter canere.

Primo. Solfisando: Hoc est syllabas seu

vocum nomina exprimendo. Secundo.

Notularum tenores cum textu eis supposito

pronunciando. Tertio. Sonos ac voces

tantum emittendo, absque textu et solfa.

Primus modus. cantum addiscentibus

habilis est, Sic enim ad rectam melodiam

vocum distinctione as[s]uescunt. Secundus

iis qui vel in choro vel alibi canere solent.

Tertius conuenit instrumentis."

(Cochlaeus 1511–14, tr. 2, ch. 6, f. B iiiiv)

The three ways of realizing music

Yet, singing happens in a threefold

manner. First, solmizing: that is, by

expressing the syllables or the name of the

voice. Second, by pronouncing the notes

[tones] of the tenors set with their text.

Third, uttering sounds and also voices,

without text or solmization syllables (solfa).

The first way (modus) is singing

appropriate to novices (addiscentes), thus,

with respect to a recta-melody, they are sure

to become used to the distinctions of the

voices [i.e., to the intervals]. The second, to

those who are accustomed to sing either in a

chorus or elsewhere. The third concerns [the

use] on instruments.

(my translation, cf. Miller 1970, 40)

In other words, the first kind would be more proper at a reading (perhaps rehearsal)

stage, and the second kind, at an actual performance or final reading stage of a given piece

of music. These first two kinds of reading apply to the same kind of group (singers), with

the same training and virtually with the same skills—therefore, no different social groups

are implied as in Gaffurius's stages. (Gaffurius's second, vocalization-like stage seems to

be either bypassed, or deemed unimportant in Cochlaeus's conception of vocal music

reading.) The third kind of reading, applied to instrumental music, is accomplished by

executing the tones without any syllables—that is, no solmization syllables are uttered, nor

syllables from any poem that may have been attached. (Even though this kind may be

compared to Gaffurius's vocalization-like stage, it finds no correspondence in that

description, for it is clearly associated with instrumental realization.) This third kind also

reveals a quite different group (instrumentalists) from the one which makes use only of the

first two kinds of reading (singers).

55

Despite the apparent restriction to singing, implied in the opening phrase "Contingit

... tripliciter canere" (loosely, "three ways that happen in singing"), instrumental music is

unquestionably included in Cochlaeus description (explicitly asserted in the last phrase of

the quotation: "Tertius conuenit instrumentis" (loosely, "the third kind is applied to

instruments"). The presence of these two phrases allows for another interpretation: that

both vocal and instrumental 'readers' were subject to the same training (schooling

background) and performance paradigm, with the resultant performance realized in different

ways. In Cochlaeus's context, instrumental practice could refer to instrumentalists

performing either with human voices, or alone. If a performance involved both human and

instrumental voices, the latter would closely follow the vocal reading down to its solmization

syllables, even if these syllables were merely thought (i.e., not explicitly uttered) by the

instrumentalists—in this situation, their practice would be subordinate (subaltern) to that of

the singers. If the performance was that of instruments alone, both reading and perception

(conceptually and aurally) of the actual sounds would be a result of some kind of

solmization—one that doubtless would conform to the same paradigm followed in vocal

music (at least as suggested in Cochlaeus's quotation). Although it appears that one cannot

be sure of which solmization paradigm was being followed, the inclusion of instrumental

reading in the same paragraph dedicated to vocal reading suggests that both groups shared

the same educational background—complete understanding and abidance to which was,

thus, not exclusive to singers. At least within the time-frame of the thirteenth to the

sixteenth centuries, there is supplementary evidence that instrumental music would have

56

followed the same paradigm used by vocal music. Even where individual notations for the

vocal and instrumental repertoire differed, the paradigm used was the hexachordal

solmization, in which ficta-steps were conceptualized (in practice as in speculative theory) as

steps that fell outside the standard collection of the recta-gamut, for their identification was

dependent on hexachordal structures associated with step-letters. The quotations below

may not constitute peremptory evidence nor pervasive acceptance of this line of thought, but

they do attest to its existence.

Videndum est de falsa musica que

instrumentis musicalibus multum est

necessaria, [...].

(Garlandia p. 1240; CS 1: 166)

It must be known of falsa musica that it is

often necessary for musical instruments,

[...].

(my translation; cf. Hibberd 1942, 219)

————————

[...] y lo que es incantable no se puede tañer.

(Sancta Maria 1565, Arte de tañer fantasía 1:

ch. 11, f. 27v; quoted in Toft 1992, 152n)

[...] and that which is unsingable cannot be

played [on an instrument].

(my translation; cf. Toft 1992, 11)

In the first quotation, Johannes de Garlandia makes clear that instruments must also

employ musica ficta when needed. In Tomás de Sancta Maria's assertion, the interpretation

of what is "unsingable" is twofold: first, it may be due to vocally unidiomatic phrases (i.e., a

melody that could not be possibly uttered by the human voice—itself allowing for

impossibilities resulting either from technical/register limitations, or perhaps because of

aesthetic issues); second, the "unsingable" may be due to phrases composed in a way that

57

would not follow (or that would challenge) the proper solmization procedures applied to

vocal realization. It is, of course, the second stance which is being emphasized here.50

As a conceivable result of the predominant vocal-solmization paradigm (based on

the Guidonian syllables), the graphic features of music notation (vocal or instrumental)

would be developed into a format that could indicate appropriate hexachordal readings (or

realization), by implying hexachordal structures. It follows that composers (and/or scribes)

50 For comments and discussions that have acknowledged the use of the same solmization

parameters for both vocal and instrumental music, see the works by Lloyd Hibberd (1942), Howard Mayer

Brown (1976; 1984), Robert Toft (1992, esp. ch. 1). The latter introduces his point of view in a clear

statement.

Apparently, these comments [on solmization and musica ficta] applied to instrumentalists as well

as singers, for I have found no evidence which suggests that a separate theoretical system existed

for instrumentalists.

(Toft 1992, 10–11)

Notice that in sixteenth-century music (the main period of research in Toft's work) many of the

available treatises focused overtly on vocal music (plainchant or vocal polyphony), so references to

instrumental music or specificities of instrumental solmization would be expectedly rare. Also,

instrumental music was still very much dependent on (or subordinate to) the accomplishments of vocal

music, and the few treatises dedicated to instrumental music kept the same kind of dependence (both in their

discourse arrangement, and available speculative arguments). Thus, on the one hand, one may consider that

the absence of an exclusive theoretical system for instrumentalists does not constitute an argument in favor

of the idea that, because there is no evidence otherwise, it may be inferred that the parameters of vocal

solmization applied also to instrumental solmization. These remarks may seem paradoxical in relation to

the opinions defended in this dissertation. On the other hand, instrumentalists certainly began their musical

education in the same way as any other performer. Even if there were separate solmization systems for

instrumentalists and singers (which seems unlikely at this point), they would still have the same

foundation, and one group would partake of the same precepts for the understanding and the notation of

musica ficta used by the other group.

58

would likely have strived to provide indications of hexachordal solmization, either in actual

notation, or even before, in the compositional process.51

(iii) Recognition and Reading of Hexachords

First, we shall examine the basic procedures involved in solmizing a piece of music,

according to medieval tradition. As seen in chapter 1, the primary means for the solmization

of a hexachord is the identification of its internal semitone (whether or not it is marked by

means of a ficta-sign), for there is only one semitone within the intervallic configuration of a

hexachord. In order to make the proper identification and perceive to what length a

hexachord can be solmized (or even whether a change to another hexachord must be

effected), it is the melodic context that will need to be inspected for the presence (implicit or

explicit) of that internal semitone. This inspection must take two aspects into

consideration: (a) one of macro proportions (concerning the melody as a whole); and (b)

one of fairly micro proportions (concerning a simple melodic gesture). The melody must

be inspected as whole in order to determine the solmization-realm to which the entire

melody is set—i.e., whether the entire melody stays only within the recta-realm, or within

that of the ficta-realm, or even if the melody gravitates between both realms. Each 'melodic

gesture' must be inspected in order to determine the hexachord that will serve to its

51 The analytical interpretation of Machaut's Rose, lis by Daniel Leech-Wilkinson (1984) must

be mentioned as one the most compelling discussions on the role of solmization in the compositional

process.

59

solmization—this is virtually equivalent to inspecting whether or not a single 'melodic

gesture' indicates the semitone unambiguously.52 The melodic gesture is, thus, the smaller

intervallic span through which one hexachord can be solmized.

In the macro inspection, if the melody pertains to the recta-realm exclusively, a

ficta-sign will be needed only when the melodic gestures are not clear enough with regard to

the position of the semitone, otherwise no ficta-sign is needed—even in a solmization

according to a recta -hexachord (the only recta type to contain the step -fa or its octave

-fa). If the melody includes hexachords that pertain to the ficta-realm, then some

ficta-sign will always be needed, whether or not the semitone is clearly implied in each

melodic gesture. The conspicuous statement of a ficta-sign may be done during the course

of the melody, or at the signature level, and even restated when there is a need to eliminate

occasional ambiguity.

52 The concept of 'melodic gesture' given here is akin to the generic meaning of the term

'neuma,' according to Guido d'Arezzo's usage—even though this was only one of its meanings, as asserted

by Dolores Pesce.

The word neuma assumes different meanings in Guido's writings. In discussions of notation, it is

a notational symbol. In other contexts it means a melodic segment or an entire melody; that

melody may be a representative formula for identifying mode such as "Primum querite."

(Pesce 1999, 361n)

This analysis is appended to a passage on Guido d'Arezzo's Regule rithmice, where he asserts that

similarities and distinctions between different ecclesiastical modes, and their characteristics, may be traced

by observing that each finalis of each mode has its own particular 'neuma,' using later (with the same

meaning) the term 'formula tonorum vel modorum ' (i.e., 'formulas of tones or modes')—cf. (Pesce 1999,

358–363). In accordance with Guido's concepts, the 'melodic gesture' (or 'neuma') may be understood as an

occurrence that gives way to deducing modes as much as it does to deducing hexachords.

60

The micro inspection of the melodic gesture is one of the means to work through

(and eventually to discern between) all these macro-variables, including occasional changes

from one hexachord to another. It is necessary, however, to interpret what the hexachordal

possibilities are that may be drawn from different melodic gestures. The most basic case to

be inspected is that of melodic gestures whose compass includes only one semitone and,

therefore, call for the solmization of only one hexachord—thus, for gestures ranging from a

major sixth to a minor second.53 Naturally, the very first situation to consider is that of a

melodic gesture whose compass is a tonus-cum-diapente (major sixth), since that is the

range of a Guidonian hexachord.

8

:

Pu

ut

–

sol

er

sol

na

sol

–

la

–

sol

tus

fa

est

fa fa fa

no

sol

–

fa

–

la

–

sol

|bis,

sol

FIGURE 2 . 1 - "Puer natus" (Introitus - mode 7)—(LU, 408). Solmization of a

-hexachord (i.e., hexachord durum).

From FIG . 2 .1 , it must be noted that in spite of lacking an explicit statement of the

internal semitone, the compass (G-e) clearly denotes the use of a recta -hexachord as a

basis for the melodic construct, and therefore for the solmization of this phrase. The

53 In this case, the inspection will discard those intervallic spans that contain more than one

semitone or only whole-tones—e.g., the minor sixth (since it contains two semitones), the major third

(since it contains two whole-tones), the major second (only one whole-tone), and the tritone. These and

other intervallic spans will be inspected in this and the following chapters—including indications of

hexachords of the same kind (i.e., whose uts are located an octave apart from each other), and issues about

changes from one hexachord to another (mutation, permutation, transmutation).

61

following illustration (FIG . 2 .2) shows another example in which the compass of the

melodic gesture is a tonus-cum-diapente (F-d), denoting the use of the recta -hexachord,

although this time both steps of the internal semitone (a-mi and fa) are explicitly stated.

8

:

O

ut

–

re

–

mi

–

re

–

mi

–

sol

–

la 3

–

fa

–

sol

–

mi

–

re

mnes

re ut re

|*

re

FIGURE 2 . 2 - "Omnes de saba" (Graduale - mode 5)—(LU, 459). Solmization of

an -hexachord (i.e., hexachord molle).

In FIG . 2 .2 , the occurrence of the fa (equivalent to modern b ) does not need

indication by the explicit means of a ficta-sign, since the gesture (its compass and context as

a mode 5 melody) gives away the appropriate hexachord to be solmized: a recta

-hexachord starting on F-fa-ut. From the above examples, it can also be observed that the

tonus-cum-diapente compass is too narrow a compass to be further inspected in most

melodic gestures, since it needs to take one specific configuration (T-T-S-T-T) to meet the

condition of denoting only one hexachord. The inspection will then fall on the intervallic

spans of a diapente (fifth) and of a diatessaron (fourth).

In FIG . 2 .3 , below, the compass (C-G) of the melodic gesture will naturally reveal

the position of the internal semitone of the hexachord to be solmized, even if only one of the

steps that frame the semitone is explicitly shown. In order to denote the recta -hexachord,

it would also be enough if that gesture presented no Fs, or even if it was only a diatessaron

in range (e.g., from C to F without the G, or from D to G without the C—the reason for this

62

is because the semitone that exists between the step-letters E and F, in either of those

diatessaron compasses, cannot be found only in the -hexachord).54 Although other

intervallic spans may serve as cues for a hexachord, the diatessaron must be emphasized as

one of the most important intervals to serve in this capacity, since it is the largest interval for

which any of its species (T-S-T, S-T-T, and T-T-S) fit inside one single hexachord—even if

54 Gaston Allaire, especially in one of the sections of his book entitled The Theory of

Hexachords (1972, 16–32), went on to devise a whole "theoretical basis" for solmization and for musica

ficta, in which he mentions that fourths and fifths are the most appropriate intervallic ranges of a melodic

gesture to serve for the deduction of hexachords. He ultimately defends that the fourth would be the basis

for such a deduction, and therefore the basis to effect solmization—he implies specifically that the lower

tetrachord (ut through fa) of a hexachord is the most needed for such identification.

[I]n order to form ut one must have a fourth. This fourth may not be written down in notes, but it

must be implied. [...] The fourths and fifths are the key intervals of the hexachord system, i.e. they

are the intervals that determine the hexachords, and it is not without reason that medieval and

renaissance treatises define and illustrate them at length.

(Allaire 1972, 24)

One certainly has to agree with Allaire, in that fourths and fifths are indeed the "key intervals"

through which one can explain the intervallic construction of hexachords, and therefore use them not only

to recognize hexachords, but also to implement solmization, since these intervals will always contain one

semitone. Allaire bases his assertions mainly on a late-sixteenth-century French treatise by Jean Yssandon,

entitled Traité de la musique pratique (1582), in which the author attempted a description of the three basic

types of hexachords (molle , durum, and naturale) by stating what their steps at the beginning, mean, and

end are (i.e., respectively at their ut-position, fa-position, and la-position). Yssandon, nevertheless, was

merely providing descriptions of deductions and proprieties (genres or especes, in his words), informed not

only by the same kind of discourse used by many previous theorists (e.g., Garlandia, Anon. 2,

Tinctoris—quoted earlier in chapter 2 [i]), but also by a tentative inclusion of his own personal and

humanistic motivations. Also, it is not for the purpose of instructing readers about hexachordal

solmization that ancient theorists took the time to discuss those intervals "at length" (as Allaire seems to

suggest), for the hexachord (or rather, the step-designations that included solmization syllables) was merely

a means of identifying the steps. Rather, those theorists did so because these intervals (fourths and fifths),

included among the perfect consonances, had to be thoroughly defined and illustrated, since they are the

natural divisions (formants) of a more basic and more perfect consonance: the octave (diapason), the

understanding of which (and of its species) is the essential element (and link) that provides a background for

the descriptions of modes, hexachords, and intervals.

63

the actual compass of the melodic gesture is larger, the diatessaron span will help deducing

the hexachord.

: re fa fa fa sol fa re ut re re ut

FIGURE 2 . 3 - Recognition of hexachords (fifth-span melodic gesture without an

explicit semitone). Solmization of a -hexachord (i.e., hexachord

naturale).

Medieval and Renaissance theorists were accustomed to describing these three

species of the diatessaron by means of specific sequences of solmization syllables that

revealed they could pertain to one, and only one, hexachord.

Diatessaron interpretatur de quattuor; [...],

constans ditono et semitonio, ut a .Γ. ad .C.

Est autem diatessaron trimodum verbi gratia

ut fa re sol mi la.

(Affligemensis ca. 1100, ch. 8; Smits van

Waesberghe 1950, 69; GS 2: 238;

PL 150: 1399)

Diatessaron means "four," [...]; it contains a

ditone and a semitone, as from Γ to C.

Moreover there are three species of

diatessaron: ut–fa, re–sol, and mi–la.

(Babb 1978, 111)

————————

De consonantia diatessaron et eius speciebus.

Caput quintum.

Diatessaron est consonantia quattuor

sonis duos tonos et minus semitonium

circumscribentibus ducta: [...] tres igitur ut

dictvm est diuersas species seu figuras

compraehendit. Prima pertransit ex graui in

acutum toniaeo semitoniaeo ac toniaeo

interuallis harum circumscriptione

Chapter 5 — Of the consonance of the

diatessaron and its species

The diatessaron is a consonance of four

steps, defined by two tones and a minor

semitone; [...] it consits of three different

species (or figures). The first extends from

low into high by intervals of a tone, a

semitone, and a tone, marked off by these

syllables: re mi fa sol [...].

64

syllabarum re mi fa sol: [...].

Secunda diatessaron figura procedit ex

graui in acutum semitonio ac duobus conti-

guis tonis distincte et composite dispositis.

his scilicet syllabis: mi fa sol la [...].

Tertia diatessaron forma tenditur a graui

in acutum [...]: his syllabis vt re mi fa: tono

scilicet ac tono atque semitonio [...].

(Gaffurius 1496, bk. 1, ch. 5, f. b iv)

The second species of diatessaron

proceeds from low into high by semitone

and two successive tones, clearly and

deliberately arranged by these syllables,

namely: mi fa sol la [...].

The third form [species] of diatessaron

stretches out from low into high [...]; by

means of these syllables: ut re mi fa, namely

by tone, and tone, and semitone [...].

(my translation; cf. Miller 1968, 42–43;

Young 1969, 36–37)

The two treatises quoted above (Johannes Affligemensis's De musica, and

Franchinus Gaffurius's Practica musice), dated approximately four centuries apart, attest to

that kind of solmization in describing the different species of the diatessaron. Despite this

evidence, nothing prevents a diapente or a tonus-cum-diapente to serve as cues for

solmization in specific situations, for the indication for one sole hexachord is unequivocal in

the case of two of the four species of diapente (i.e., T-T-S-T, and T-S-T-T, respectively

described in historical treatises through the syllables ut-sol, and re-la), and by one of the

five species of tonus-cum-diapente (i.e., T-T-S-T-T, described through the syllables

ut-la).55 When the compass is not as large as a diatessaron, it may suffice to locate the

span of a semiditonus (minor third), for it will also unequivocally reveal the internal

semitone of a specific hexachord through its two species (T-S, and S-T) traditionally

55 The other species of the diapente and of the tonus-cum-diapente can serve well as indications

that some change from one hexachord to another is underway.

65

described with the syllables re-fa and mi-sol.56 When the semitonium (minor second—i.e.,

the internal semitone itself) is explicitly shown, the compass of the whole melodic gesture

must still be carefully observed, for it is not enough to know 'what hexachord to solmize' at

one point, it is also necessary to know 'for how long the deduced hexachord can be

solmized' before a change to another hexachord is needed. The following illustration

(FIG . 2 .4) may serve to illuminate further the above discussion. It presents a full

solmization for the Hymn to St. John ("Ut queant laxis"), in which the recta -hexachord is

clearly indicated by the individual melodic gestures corresponding to each of the verses (the

first verse begins with the words "Ut queant," the second begins with "Mira," and the third

begins with "Solve"), as well as by the final melodic gesture set to the vocative-like line on

the name of "Sancte Johannes." Since the melodic gestures provide solmization and

recognition of one, and only one, specific hexachord, there is no need in the course of the

hymn to change the solmization (i.e., to make a mutation) to a hexachord other than the one

implied by its first melodic gesture.57

56 As mentioned above, the ditone (major third), which has only one species (T-T), will not

point to a definite hexachord, but it will present only the lower or upper part of a hexachord—i.e., its ut-mi

portion or its fa-la portion. These portions of a hexachord are generally used and preferred as locations for

possible mutations to a different hexachord—this will be made clear in the following chapters.

57 These features make all the more meaningful this Guidonian version of the Hymn to St. John,

in regard to its role and transmission as a pedagogical tool. In most of the extant forty-seven manuscripts

that contain a copy of the Ut queant laxis melody, the gestures clearly done indicate a solmization according

to the low recta -hexachord. In four manuscripts, the solmization must follow the recta -hexachord

(D-Kl 4º Mss. Math. 1; US-Malibu, J. Paul Getty Museum Ludwig XII 5 [olim Phillipps 12145]; F-Pn

lat. 7211; F-Pn nouv. acq. lat. 443)—this latter manuscript also presents a transposition to the recta

-hexachord, and another version that entails mutation between two recta-hexachords ( and ). In only

three of the forty-seven manuscripts, the melody does not conform to the solmization of only one

66

!

8

:

Ut

ut

que-

re

ant

fa

la

re

–

mi

xis

re

re -

re

so-

re

na-

ut

re

re

fi -

mi

bris

mi

Mi

mi

–

fa

–

sol

ra

mi

8ges -

re

to

mi

–

ut

rum

re

fa -

fa

mu -

sol

li

la

tu

sol

–

fa

o -

re

rum,

re

Sol

sol

–

la

–

sol

ve

mi

8pol-

fa

lu -

sol

ti

re

la -

la

bi -

sol

i

la

re -

fa

a

sol

–

la

tum,

la

San

sol

–

fa

cte

re

Jo -

ut

han-

mi

nes.

re

FIGURE 2 . 4 - "Ut queant laxis" (Hymnus - mode 2)—(Pesce 1999, 466; cf. LU,

1504). Solmization according to the -hexachord (i.e., hexachord

naturale).

The above discussion about the inspection of melodic gestures can be summarized

thus: the main compass to look for is first the diatessaron, then see if it can be expanded to

the appropriate species of the diapente, or even of the tonus-cum-diapente, in order to learn

how far the deduced hexachord can be solmized; if, however, the diatessaron-span is not

hexachord, and needs mutations involving the - and the -hexachord s (in two manuscripts the melody

starts on Γ-ut: CH-Geneva, Bodmeriana lat. 77 [olim Phillipps 188845], and A-Wn 2503; and in one it

starts on C-ut: F-Pn nouv. acq. lat. 443). Since in some manuscripts the melody is presented in duplicate

or triplicate, it amounts to a total of fifty-five versions—some of which are non-transposed with variants,

others are transpostions with or without variants (in all cases, however, these are only minor variants).

This brief survey was based on Dolores Pesce's edition and translation of the Epistola ad Michahelem—for

this and other assessments regarding the pedagogical role of the melody cf. (Pesce 1999, 19–38, 547–554).

67

conveniently presented, the semiditonus-span can be alternatively used as a cue for an

individual hexachord.

Nevertheless, the presence or absence of ficta-signs still remains to be investigated

in relation to medieval and Renaissance tradition. As shown above (FIG . 2 .2), when a

melodic gesture (compass and mode contexts) is sufficiently clear in their indication of the

recta -hexachord, then there will be no need for notating a fa-sign. The absence of any

ficta-signs (either fa- or mi-signs) in that particular situation does not, however, indicate that

signs are always (nor even generally) unnecessary, for this kind of absence applies only to

those circumstances in which the melodic gesture is clear, or where there are no phrases

involving the ficta-realm. In order to illustrate this issue, four treatises will be quoted below:

the Berkeley anonymous (1375), Prosdocimus de Beldemandis's Contrapunctus (1412),

Johannes Gallicus's Ritus canendi vetustissimus et novus (1458–64), and Tinctoris's Liber

de natura et proprietate tonorum (1476).

Unde cuiuslibet deduccionis cantus habens

originem in C cantatur per naturam, in F per

b, in G per #. Circa hec sciendum est quod

in cantu inveniuntur duo signa, scilicet

signum B mollis et signum B quadrati,

demonstrancia ubi fa et mi debeant cantari, et

possunt poni in diversis locis manus, ut

patebit inferius de coniunctis, sed ipsa

frequenter sunt in B-fa-B-mi, virtualiter licet

semper non signentur. Pro quo nota quod

quandocumque ab vel de sub F-fa-ut

ascenditur usque ad b-fa-#-mi mediate vel

immediate, et iterum descenditur usque ad F-

fa-ut priusquam ascendatur ad C-sol-fa-ut,

debet cantari fa in b-fa-#-mi per b, nisi

A song in any hexachord originating on C is

therefore sung in natural form, on F with a

b, and on G with a #. In regard to these

things, it must be known that two signs are

found in song--the sign B mollis and the

sign B quadratum--which show where fa and

mi ought to be sung; they can be placed in

different locations in the hand--as I shall

explain later concerning coniunctae, but they

are frequently on B-fa-B-mi. In general, it is

not necessary to notate them. For that

reason, note that whenever one ascends from

(or from below) F-fa-ut to b-fa-#-mi,

indirectly or directly, or when one descends

to F-fa-ut before ascending to C-sol-fa-ut, he

68

cantus finiat in G basso.

(Anon. Berkeley 1375, tr. 1;

Ellsworth 1984, 44)

ought to sing fa on b-fa-#-mi (by b), unless

the song should end on G bassus.

(Ellsworth 1984, 45)

————————

[...], de qua ficta musica est primo

sciendum quod ipsa nunquam ponenda est

nisi loco neccessitatis, eo quod in arte nichil

est ponendum sine neccessitate.

Item sciendum quod ficta musica

inventa est solum propter consonantiam

aliquam colorandam, que consonantia aliter

colorari non posset quam per fictam

musicam. Et ex istis duobus notabilibus

apparere potest quomodo quasi omnes

cantuum compositores circa hanc fictam

musicam sepissime errant, quoniam ipsa

multotiens utuntur in loco ubi non est

neccessitas, sicut verbi gratia quando ad

clavem de natura ponunt b rotundum sive

molle, scilicet in Elami gravi, [...].

(Prosdocimus 1412, bk. 5; Herlinger 1984,

70–74 [even]; cf. CS 3: 198)

[...]. Concerning musica ficta, it is

necessary to know first of all that it is never

to be applied except where necessary,

because in art nothing is to be applied

without necessity.

It must be known, too, that musica ficta

was invented exclusively for the sake of

coloring some consonance that could not be

colored except by musica ficta. From these

two points it can become evident that almost

all composers of song very often err with

respect to musica ficta, since they very

frequently use it were [sic, where] there is no

necessity--as for instance when they apply

the round or soft b in a natural signature--as

on low Elami, [...].

(Herlinger 1984, 71–75 [odd])

————————

Quintus tonus ex tertia specie diapente

et tertia diatessaron superius, id est supra

ipsum diapente, formatur [...].

Sextus autem formatur ex tertia specie

diapente et tertia specie diatessaron inferius,

hoc est infra ipsum diapente [...].

[...]

Ut autem evitetur tritoni durities,

necessario ex quarta specie diapente isti duo

toni formantur. Neque tunc mollis signum

The fifth tone [i.e., mode Tritus

autenticus] is formed from the third type of

the diapente and the third type of the

diatessaron above, that is, above that

diapente [...].

The sixth tone [i.e., mode Tritus

plagalis], on the other hand, is formed from

the third type of the diapente and the third

type of the diatesssaron below, that is,

below that diapente [...].

[...]

In order to avoid the harshness of the

tritone, however, by necessity these two

tones are formed from the fourth type of

69

apponi est necessarium, immo si appositum

videatur, asininum esse dicitur.

(Tinctoris 1476, ch. 7-8; CS 4: 21–22; Seay

1975–78, 1: 73–74)

diapente. Nor then is it necessary that the

sign of soft be added; rather, if it is seen to

have been added, it is said to be asinine.

(Seay 1976, 9–11; cf. Berger 1987,

162–163; Urquhart 1998, 4)

[Interpolations mine]58

These treatises (and particularly those passages) have been frequently quoted in

musicological studies as evidence for the interpretation that it was a fairly common

procedure to leave those ficta-signs unnotated, or even that ficta-signs should best be

avoided rather than explicitly notated. Nevertheless, in all three treatises, following their

own melodic references, the authors are actually discussing signs applied to recta-realm

contexts. The Berkeley anonymous describes three basic melodic gestures: (a) ranging

from F to b (clearly presenting the lower diatessaron of an -hexachord); (b) ranging from

F to c (expanding that lower diatessaron to a diapente, also denoting the use of the

-hexachord); (c) ranging from G to c, that is, stopping on G in its descent from c (thus the

lower diatessaron of the -hexachord, and not the -hexachord).59 There is also another,

58 In Seay's edition, there is a minor typographical error on the word "asininum," which has been

written with the spelling "asinimum"—Coussemaker's edition gives the correct spelling.

59 In a footnote to his translation of the treatise, Ellsworth (1984, 45) provides a somewhat more

literal interpretation of the final descent to G. He asserts that it is a reference to a melody whose finalis

would be G (i.e., the tetrardus modes), warning that if the introduction of a -fa was to occur, it would effect

an alteration to the mode, since it "would reproduce around G the intervallic pattern of the first and second

mode." Although the anonymous author of the treatise may have taken the opportunity to anticipate a

presentation on modes, the passage under consideration (at the beginning of the tractatus primus) is mainly

dedicated to the introducing the gamut, hexachords, and some solmizatio principles—it does not include

presentations or direct references to modes, and comes after assertions that "all song in the world ought to

be sung by one of" the three proprieties (natura, durum, molle); "Omnis [...] cantus mundi debet per

aliquam ipsarum proprietatum [...] cantari" (Anon. Berkeley 1375, tr. 1; Ellsworth 1984, 44, [trans.] 45),

70

less-conspicuous melodic gesture, ranging from below F to b, which must be divided in two

parts, demanding at least two different hexachords for its solmization: the -hexachord for

the F-b compass itself, and perhaps the -hexachord for the compass below the F—there is

no way of determining the precise hexachord for the lower part of the gesture, since no

other steps are mentioned in the text, leaving the compass below F indeterminate.60 In

Prosdocimus's assertions, the recta-realm is established at the end of the quotation, where it

mentions that no fa-sign should be used "ad clavem de natura"—i.e., at a melodic gesture

that calls for the solmization of a -hexachord.61 It is unclear whether the Prosdocimus

assertion is an indication of a fa-sign ( ) placed on the E-location or on the b-location in the

staff, but it is certainly unnecessary since it would change the solmization of the referred

in the translation Ellsworth gives "property" for "proprietas," instead of "propriety." In any case, whether

or not there are references to modes, it does not contradict the understanding of that quotation as a

description of melodic gestures (in order to indicate the need for a -fa solmization)—for the identification of

melodic gestures and modes are complementary elements used to inform solmization.

60 The indeterminacy of the compass below F is certainly justifiable, since neither is the change

from one hexachord to another being discussed at this point in the work, nor is the use of the naturale

hexachord. The main subject of the treatise at this point is the inspection of gestures that express the molle

or durum hexachords, and how they may or not need the notation of ficta-signs—these have no meaning for

the naturale hexachord, for it contains no b, and its solmization never entitles the use of a any sign.

61 In the quotation given above, the phrase "ad clavem de natura" has been translated by Herlinger

as "in a natural signature." This translation should not be taken as a reference to some kind of

'key-signature,' or even 'clef' in the modern sense, for the latin phrase refers rather to the hexachord naturale

(or more properly, to a melodic gesture that takes its solmization from the -hexachord). In order to

provide an unbiased interpretation, the Lexicon Musicum Latinum Medii Ævi gives that passage from

Prosdocimus's treatise is given under: Clavis, IV (note, letter that indicates a note, name of a note,

placement of a note), B (with no specific meaning), 6 (when one note encompasses both the pitch itself and

its altered form [raised or lowered by a half step])—cf. (LmL 5: 536). (There were indeed ficta-signs

appearing at signature positions, but those occurrences did not have the same meaning as modern

key-signatures, for they were rather indications of a shift in the group of three hexachords whose

solmization is expected by default—see chapter 8 [iii].)

71

melodic gesture, from the -hexachord to the -hexachord. If the sign was placed on the

E-location itself, it would call for the creation of a ficta E-fa, but if the sign was placed on

the b-location (thus using the solmization fa on -fa / -mi), it would still change the original

recta E-la-mi into the ficta E-fa (lest the recta E-mi could establish a melodic tritone with

-fa), and consequently affect the entire realm of the melody. In the last quotation, Tinctoris

discusses the need to avoid the tritone in tritus-mode melodies, asserting that the third

species of the diapente (which serves as a basic formant for the tritus modes) must be

changed into its fourth species when the tritone is presented. This situation remains

characterized as one pertaining to the recta-realm, and so there is really no meaning for an

explicit (pleonastic) indication of the fa-sign, since most tritus melodies naturally contain

gestures expressed by the diatessaron F-b, or even by the diapente F-c, which call for a

solmization according to the -hexachord (the recta-step -fa being implicit).62

62 In a paper read at the annual AMS meeting in Boston (1998), Peter Urquhart argued that the

three theorists quoted above are the only ones to provide statements that signs are unnecessary. There is,

however, at least one other treatise that contains assertions similar to those of Tinctoris, from Johannes

Gallicus's Ritus canendi, which has been quoted in this same capacity by Karol Berger [ellipses mine].

Dicunt namque nostri moderni non cantemus per molle, nisi sit signatum, et alii dicunt imo

cantemus cum dulce sit magis quam quadrum, sic musicam ut vina probare putantes. Quae

quaeso frivola sunt haec carissimi, quaeque pueriles ac insipidae nimis opiniones? Ergo ne psalmos

introituum de quarto tono carere debemus per quadrum, qui toti iacent in tritono, dulcesque sancto-

rum et angelicas magisquam humanas modulationes ob nostram ignorantiam duras atque rusticanas

reddere? Si nobis non licet absque signo puerorum ac rudium bene canere, non liceat etiam absque

signo tubarum aut campanarum manducare. [...]. Sint ergo signa mollis et quadri pro pueris et

qui non intelligunt tonum ac semitonium rudibus, nos vero sectari decet rationem, [...].

(Gallicus 1458–64, pt. 2; CS 4: 360–361; Seay 1981, 28)

For our moderns say that we do not sing through the soft b unless it is written and others say that

we do it when it is sweeter than the square b, thus imagining to test music like wines. I beg you,

72

The quotations given here take melodic instances as the bases (or even paradigms)

for the discussion of solmization, and for the appropriateness of notating ficta-signs, thus

emphasizing the idea that solmization even in polyphonic music depends primarily on the

melodic gesture (and not only on relations between voices). This approach promotes the

idea that musica ficta (in its dependence on adequate solmization) had its origin in

monophonic music, and continued to be executed primarily according to that same

parameter, although ficta-occurrences (as any other element of solmization) could include

interpretations according to contrapuntal rules. Also, those quotations do not indicate that a

ficta-sign should be omitted when it is needed, but only when (observed the hexachordal

indication given by the melodic gesture) it is not needed. Although the statements are

limited to a discussion of signs applied to the double-step -fa / -mi (i.e., in a purely

musica recta context), one can easily transfer the same precept to a context in which

ficta-hexachords were involved. In a recta-context, a melodic gesture will take solmization

according to one of the three recta-hexachords (either -, -, or -hexachord), and it may be

my most loved ones, what sort of trifles are these, and what sort of childish and exceedingly

insipid opinions? Then should we sing the psalms of introits of the fourth mode, which lie

entirely within the tritone, through the square b and render the sweet and more angelic than human

melodies of saints harsh and rustic because of ignorance? If we are not allowed to sing without the

sign of boys and uncultivated people, it would not be permitted also to eat without the sign of the

trumpets and bells. [...]. Therefore, let the signs of the soft b and square b be for boys and those

uncultivated people who do not understand the whole tone and semitone. It behoves us, however,

to follow reason, [...].

(K. Berger 1987, 162)

The context of Gallicus's discussion (as in the other works quoted above) is one that promotes the

use of the solmization fa at the b-location when there is a need to avoid tritones, but considers that the

melodic gestures involved are generally deemed enough as indications for that solmization, and that

ficta-signs are virtually unwarranted.

73

even possible that the different gestures of a single melody will call for the solmization of all

three. Still, none of these solmizations will necessarily require the presence of signs for the

syllables fa or mi, provided the gestures make conspicuous indications of the semitone

within each hexachord—signs are needed only when the gesture is ambiguous with regard

to the appropriate (or intended) hexachord. Now, considering a ficta-context, some

ficta-sign will always be needed in order to serve as an indication for the internal semitone

of the ficta-hexachord intended for solmization, but it is the melodic gesture that will provide

the final determination for the hexachord to be solmized. This is valid whether the melody

as a whole is made of hexachords exclusive to one realm (ficta or recta), or whether it is

made of hexachords that alternate between the two.

: mi sol sol sol la sol mi re mi mi re

FIGURE 2 . 5 - Recognition of hexachords (fifth-span melodic gesture without an

explicit semitone). Solmization of a -hexachord

(ficta-hexachord of the molle family).

The illustration above (FIG . 2 .5) is based on FIG . 2 .3 , which has been altered to

include a fa-sign ( ) on the E-location—thus calling for a solmization as E-fa, according to a

ficta -hexachord. Despite the presence of a sign on the E-location, the step E-fa is not

performed in the melody, for the sign is only an indication of where the internal semitone

is—in this case, between E-fa and D-mi. Notice, also, that the actual positioning of the sign

is not irrelevant, for it may be interpreted as an indication of which melodic gesture should

74

take the solmization of the ficta-hexachord being represented by that sign, or even as an

indication of where the solmization of the ficta-hexachord should start.63 When a

solmization includes a ficta-hexachord, the hexachordal possibilities are expanded beyond

the limits of the three basic hexachords ( -, -, and -hexachords)—i.e., beyond the limits

of the recta-realm, and toward the inclusion of at least one extra hexachord. The presence

of a ficta-hexachord may also imply that some transposition of the recta-realm, while

maintaining the available number of hexachords to be chosen for solmization to only three,

i.e., a group of three hexachords transposed from the three basic ones, but maintaining the

intervallic relation of fourth between them. For instance, in a hybrid recta-plus-ficta context,

the hexachords at work could be -, -, and -hexachords; in an exclusively ficta context,

those three hexachords could consist of -hexachord, -hexachord, -hexachord.

(iv) Equivalence Between Hexachords

It may also happen that the intervallic span of a single melodic gesture exceeds the

limits of the hexachord being solmized. Strictly following medieval theory, any step that

falls beyond the hexachordal limits should be solmized according to a different hexachord.

However, the steps involved in the gesture may pertain to hexachords of the exact same

kind—i.e., hexachords whose uts are applied to step-letters located one octave apart from

63 The position of ficta-signs as indications for solmization shall be discussed in subsequent

chapters.

75

each other. For instance, a melody can be composed according to a recta -hexachord

starting on C-fa-ut, and include steps above that pertain to another recta -hexachord

starting on c-sol-fa-ut, and even steps below that pertain to a ficta -hexachord starting on a

fictitious CC under Γ. This is a situation in which the participating hexachords are the same

(disregarding their octave), and their generic kind ( -hexachord) is never abandoned—in

effect, they are octave-equivalent hexachords, and no actual change to different hexachord is

being implemented. (In FIG . 2 .6 , and throughout this dissertation, underlined solmization

syllables will be used for those occasional outside steps that find octave equivalence within

the main hexachord—i.e., steps that pertain to octave-equivalent hexachords.)

: refa fa sol mi fa mire

|

ut ut sol la sol fa

|

reut re la ut re ut fa mire

FIGURE 2 . 6 - Octave equivalence (melodic gestures exceeding the hexachordal

limits). Solmization of a -hexachord (i.e., hexachord naturale).

The example shows that the main -hexachord being solmized has its ut on C-fa-ut,

but two steps, outside that hexachord, also occur: the recta c-sol-fa-ut solmized as ut, and

the ficta A-la-mi solmized with the new syllable la. In the situation proposed in FIG . 2 .6 ,

the octave equivalence ensures that a specific hexachordal solmization is not changed when

the melodic gesture exceeds the span of six steps (tonus cum diapente), provided the

correspondent octave of all the exceeding steps can be found within that main hexachord.

These octave-equivalent solmization syllables can be effected, however, only when the extra

76

steps demonstrate transitory or momentary digressions from the main hexachord being

solmized—when the extra steps generate a melodic gesture of their own, a change to another

hexachord must be implemented. Other solmizations, facilitated by the use of the

octave-equivalence concept, are exemplified below in FIG . 2 .7 (drawn from the beginning of

Phillippe Caron's Accueily m'a belle) and FIG . 2 .8 (drawn from the mode 1 Kyrie eleison

from the Mass Orbis factor)—in both examples, the final melodic gesture demonstrates the

need for a change (mutation) to a different hexachordal solmization. (The mutation is

represented by solmization syllables bearing the 'equals' sign [=], those syllables enclosed

in brackets are not to be uttered, only aurally conceived, whereas the syllables not enclosed

in brackets are the ones actually solmized on those steps.)

8

Contratenor

[ Ac-

: sol

cueil-ly m'a

mi ut sol

la bel – le

sol sol mi re= : [=sol]

au-gent a– ]

[sol=]=ut ut mi

FIGURE 2 . 7 - "Accueily m'a belle" (contratenor only), 3-voice rondeau by

Phillippe Caron—(Mellon Chansonnier, f. 3v). Solmization of

an -hexachord, and a subsequent mutation to a -hexachord.

In FIG . 2 .7 , the first hexachord being solmized is an -hexachord whose ut falls on

F-fa-ut, and whose sol falls on c-sol-fa-ut. The fourth note, on the "m'a," falls on the

step-letter C, and may be solmized with sol, thus constituting a ficta-step C-sol (exceeding

the limits of that first -hexachord), which may be conceived in two ways: either as a

lower-octave equivalent to c-sol-fa-ut; or as the sol pertaining to the lower-octave ficta

77

-hexachord, equivalent to the original recta one). The same C-sol is also used later, on the

word "augent," to serve as a point of departure to a new hexachordal solmization, producing

the recta-step C-ut (first step of the -hexachord). That last sequence of steps C-C-E

establishes the beginning of a new melodic gesture that departs completely from the initial

-hexachord, thus inducing a solmization change to the -hexachord.

! 1 .

K

8

3

y – ri

: mifa mi

|

– e

remi la

e – –

ut remi 3

– – –

fa mire :

– – –

[ut=]=fa mire

le -i-son

ut re re

FIGURE 2 . 8 - "Kyrie eleison" (mode 1), from Mass XI "Orbis factor"—(LU,

46). Solmization of an -hexachord, and a subsequent mutation to

a -hexachord.

In FIG . 2 .8 , the sixth step (last one on the word "Kyrie") should be solmized to the

syllable la, thus constituting the ficta-step D-la (according to a ficta -hexachord that would

start on an imaginary FF-ut below Γ). The sound of that ficta D-la is the same as the recta

D-sol-re that will provide the syllable re (according to the recta -hexachord) solmized in

the last gesture of that example (on the word "e-le-i-son"). In these latter two examples

(FIGS. 2 .7 and 2 .8), the first hexachord (a recta -hexachord) is indicated both by the

melodic gesture and the signature -fa, then showing a momentary detour to an

octave-equivalent ficta-step, but returning to its recta-hexachordal path, and later, a new

melodic gesture indicates a change (mutation) to a different hexachord (recta -hexachord).

78

The octave-equivalence concept finds more concrete evidence in a polyphonic,

two-voice setting presented by Johannes Gallicus, and based on a version of the plainchant

Ave Regina caelorum. The transcription below (FIG . 2 .9) shows only the last verse ("O

Maria flos virginum, Ora pro nobis, Dominum") of the contratenor from that setting.

[Contratenor]

O Ma - ri - a

re mi re ut

flos vir – – gi -num,

fa la sol fa mi re

O - ra pro no -

re mi re re

bis

la

Do - mi – – – num.

sol sol re mi fa sol

FIGURE 2 . 9 - "Ave Regina caelorum," (contratenor part) excerpted from

Gallicus's Ritus canendi (1458/64, pt. 2, bk. 3)—cf. (Seay 1981b,

14: 88; cf. CS 4: 395). Solmization syllables are original.

In Gallicus's original example, the contratenor is provided with fully designated steps

(letter-plus-syllable), in lieu of note-shapes, placed directly on the staff in a

heightened-notation fashion—the transcription below presents note-heads with the syllables

placed above the staff.64

64 There are two editions for Gallicus's Ritus canendi: one by Coussemaker (CS 4: 298–396);

and one by Albert Seay, in two volumes (Seay 1981b, 13: 1–78; 14: 1–89). For the example transcribed

here, Coussemaker presented both voices of the polyphonic setting on a 9-line staff, with handwritten F-3

and C-5 clefs, and printed letters g and d (placed as additional G-7 and D-9 clefs) apparently supplied by the

editor—the text is given below the staff, with one spelling variant on coelorum. Seay presented each voice

on an individual 5-line staff, generally with the tenor given on the lower (F-4 clef) staff, and the contratenor

79

The illustration below (FIG . 2.10) presents a clearer octave-equivalence and

hexachordal outline of the passage above. The syllables submitted to octave equivalence in

Gallicus's solmization have been underlined (as proposed in this dissertation), and each new

hexachord have been properly indicated. The exact position of changes from one

hexachord to another are also established according to the syllables prescribed by Johannes

Gallicus, since one given step-designation (letter-plus-syllable) can pertain to only one

hexachord. The octave-equivalent concept is also deduced from the syllables proposed by

Gallicus—in this dissertation, octave-equivalent syllables are underlined. On the syllables

"no-bis Do-minum," Gallicus would likely have intended a change from the -hexachord

whose ut is placed on Γ-ut, to the -hexachord whose ut is placed on G-sol-re-ut, but since

it is a simple change between octave-equivalent hexachords, the indication does not present

an actual mutation, only an equivalence. The octave equivalence is broken on the first note

(g) on the syllable "Do-mi-num," showing a momentary mutation to the -hexachord by

uttering only one of its syllables (sol). Notice that Gallicus did not choose to have that

g-step solmized ut according to the last -hexachord he used in the solmization of the

on the upper (C-1 clef) staff—the Ave Regina caelorum text is given between the staves. Since there are

some instances of crossing between the two voices, in Seay's edition the two voices may temporarily

migrate to the other staff. With respect to FIGS. 2 . 9 and 2 . 1 0 , Seay used the lower staff for the

'contratenor' on the words "O Maria flos virginum, Ora pro no-(bis)," and the upper staff from that last

syllable "-bis" onward. In both editions, while the 'contratenor' of this two-voice setting is presented in

that heightened-notation fashion, the plainchant tenor is given without solmization-syllables, but with

non-mensural note-shapes (neumae)—puncta inclinita (reserved for melismas), and virgae (reserved for

individual syllables, for the first note of a melisma, and for the entire melisma on the word "Dominum").

Earlier in the treatise (pt. 2, bk. 2; Seay 1981b, 14: 59; CS 4: 380), an individual presentation of the

plainchant was provided, with solmization-syllables for each step—for a transcription of the entire

plainchant with solmization, see FIG. 6 . 7 ; for the entire two-voice setting, see FIG. 6 . 8 ; for variants, and

differences between Coussemaker's and Seay's edition, see notes 177 and 180.

80

passage. It could have been theoretically possible, since the recta-step g-sol-re-ut allows

for such a solmization, and could thus avoid that momentary mutation to the -hexachord.

[Contratenor]

O Ma - ri - a

: re mi re ut

flos vir – – gi -num,

: la sol fa mi re

fa

O - ra pro no -

re mi re re

bis

la

Do - mi – – – num.

sol: sol : re mi fa sol

FIGURE 2 .10 - "Ave Regina caelorum," [contratenor only] excerpted from a

two-voice setting given in Johannes Gallicus's Ritus canendi

(1458/64, pt. 2, bk. 3)—cf. (Seay 1981b, 14: 88; cf. CS 4: 395).

The solmization syllables are original to the manuscript, the

explicit indications of 'octave equivalence' and 'mutation' are not.

Therefore, if no actual hexachordal change toward the -hexachord was made, the entire

passage on the words "virginum, Ora pro nobis Dominum" could have been read

according to a -hexachordal solmization, with the octave-equivalence approach exploited to

its ultimate consequences. In this way, not only the words "vir-gi-num, O-ra pro" could be

solmized according to the -hexachord starting on Γ-ut, and "no-bis Do-" solmized with

syllables pertaining to the -hexachord starting one octave higher (on G-sol-re-ut), but the

"-mi-num" could have been solmized with syllables pertaining to the -hexachord starting

81

two octaves higher than the first (on g-sol-re-ut). This alternative situation would produce

an odd kind of solmization with successive octave-equivalence approaches implemented on

top of each other. The solmization sequence could then be indicated by the following

progression: la sol fa mi re re mi re re la sol ut re mi fa sol (in this case, the syllables

falling one octave higher than the first are being indicated by a single underline, and the

syllables falling two octaves higher than the first by a double underline). However, the aural

perception (and performance) of that alternative would be not only excessive, but difficult.

It becomes evident here that the implementation of the octave-equivalence concept is meant

as a momentary resource, for if it is needed over an extensive melodic gesture, then a new

hexachordal context must be assumed, and the proper hexachordal change applied.65

The octave-equivalence concept, in fact, is an aural resource supported by

conceptions of octave (diapason), although insufficiently addressed by modern scholarship.

Now, having discussed (from a rather practical perspective) the equivalence between

hexachords of the same family and kind by means of their octave relations, the theoretical

approach must also be presented.

65 It may be speculated whether such an excessive implementation of octave equivalence could be

more feasible on an instrumental than on a vocal performance. If that is the case, then the alternative

solution going up to two octaves of octave equivalence could be used in the particular case of the

contratenor for that two-voice version of the antiphon. Indeed, although such a polyphonic setting

(discant-like) of this plainchant would be suggestive of a vocal performance, the sole compass used for the

contratenor itself does not seem to be vocally fit. Apart from successive ascending or descending leaps, it

virtually makes use of the entire gamut, in this passage alone ranging from A-re to dd-sol, but also going

up to ee-la in another section of Gallicus's example, which seems more appropriate of an instrumental

approach—cf. FIG. 6 . 8 .

82

De consonantiarum merito vel modo

secundum Nicomachum. XVIII.

[...]. Haec enim ponenda est maxime esse

prima suavisque consonantia, cuius

proprietatem sensus apertior comprehendit.

Quale est enim unumquodque per semet

ipsum, tale etiam deprehenditur sensu. Si

igitur cunctis notior est ea consonantia, quae

in duplicitate consistit, non est dubium,

primam esse omnium diapason

consonantiam meritoque excellere, quoniam

cognitione praecedat. [...]. Igitur uni

binarius comparatus proportionem duplicem

facit et reddit diapason consonantiam eam,

quae est maxima et simplicitate notissima.

[...].

Sententia Nicomachi, quae quibus

consonantiis opponantur. XX.

[...] ut unitas in arithmeticis crementi erat

diminutionisque principium, ita etiam

diapason symphoniam reliquarum esse

principium, illas vero sibi in contraria

divisione posse constitui.

(Boethius a. 510, bk. 2, chs. 18, 20;

Friedlein 1867, 249–251; GB-Ctc R. 15.22

(944), ff. 38v–39r, 39 r; PL 63: 1210–1211,

1212 [bk. 2, chs. 17, 19])

18. Concerning the merit or measure of

consonances according to Nicomachus

[...]. The consonance whose property the

critical faculty more easily comprehends

ought to be classified as the very first and

most pleasing consonance. For just as every

single thing is in itself, so also is it

recognized by the critical faculty. Thus, if

that consonance which consists of the duple

ratio is easier to know than all the others,

then there is no doubt that the consonance of

the diapason, since it precedes the others in

being known, is the first of all and surpasses

the others in merit. [...]. The 2 compared to

1 makes the duple ratio and produces that

consonance of the diapason which is the

most excellent and, because of its

simplicity, the most knowable. [...].

20. The opinion of Nicomachus regarding

which consonances are placed opposite others

[...] as unity was the first principle of

increasing and diminishing in arithmetic, so

the consonance of the diapason is the first

principle of the remaining consonances, and

only after it, can they be set down in

opposing division.

(Bower 1989, 72–73, 74)

In historical treatises since Boethius's interpretations of the Greeks in the early

Middle Ages, the octave (recognized as the most perfect consonance after the unison) was

an essential element that served as a basis (or point of reference) for the discussion of any

musical structure, and of all the other musical elements. Thus, in book 2 of his De

institutione musica, Boethius provided unambiguous statements about the importance of the

diapason as a basis for both speculative discussions and musical knowledge in general.

83

The Nichomachean understanding (which served as a foundation for the greater part of

Boethius's work) stems from the Pythagorean root (one of the most speculative grounds in

Greek musical tradition). Later in the treatise, Boethius provides assertions of a more

practical nature, through his interpretation of Ptolemy's works. The Ptolemean

understanding (which Boethius makes use of only those sections that fit his own, more

speculative tendency) tries to integrate the Pythagorean and Aristoxenian roots. The latter

presented a foundation that valued empirical verifications within Greek musical tradition.66

Demonstratio secundum Ptolomaeum

diapason et diatessaron

consonantiam esse. VIIII.

[...], quoniam diapason consonantia talem

vocis efficit coniunctionem, ut unus atque

idem nervus esse videatur, idque Pythagorici

quoque consentiunt. Quocirca si qua ei

consonantia fuerit addita, integra inviolataque

servatur. Ita enim diapason consonantiae

additur tamquam uni nervo. [...].

Quae sit proprietas diapason

consonantiae. X.

Hoc vero idcirco evenire contendit, quoniam

diapason paene una vocula est talisque

consonantia est, ut unum quodammodo

effingat sonum, [...].

(Boethius a. 510, bk. 5, chs. 9, 10; cf.

Friedlein 1867, 358–359, 360; PL 63: 1290,

1291 [as bk. 5, chs. 8, 9])

9. Demonstration according to

Ptolemy that the

diapason-plus-diatessaron is a consonance

[...]. The consonance of the diapason

produces a conjunction of pitch such that the

string seems to be one and the same. Even

the Pythagoreans agree on this point. For

this reason, if some consonance is added to

the diapason, it is preserved whole and

inviolate, as though the consonance added to

the consonance of the diapason were added to

only one string. [...].

10. The Property of the consonance

of the diapason

Ptolemy argues that this occurs because the

diapason is almost like a single pitch, and

that it forms such a consonance by creating,

as it were, a single sound.

(Bower 1989, 169–170)

66 Cf. Bower (1989, xx–xxxviii) for more complete assessments about Nichomachus and

Pythagoras, versus Ptolemy and Aristoxenus in relation to Boethius's work.

84

In book 5, Boethius takes the speculative approach he had set as basis for

discussion in the previous books of his treatise and adds a more practical approach,

introducing a reference to actual sound, and not exclusively to numbers. In the anonymous

ninth-century treatise entitled Musica enchiriadis by contrast, the more practical, empirical

approach is conspicuously expressed.

Porro maxima symphonia diapason dicitur,

quod in ea perfectior ceteris consonantia fiat,

ut sive ab acutiore sive a graviore incipias,

vox, quam octavo ordine in celsiorem vel

humiliorem mutaveris, ad primam vocem

unisona habeatur, [...].

(Anon. ME a. 900; Schmid 1981, 31; GS 1:

163; PL 132: 971)

Furthermore, the largest symphony is called

diapason, because in itself the consonance is

made more perfect than in the others, so that

whether you begin on a higher or on a lower

[place], the voice (vox, i.e., sound), which

you may have mutated according to the

octave into a loftier or humbler [voice], may

be held [as] a unison to the first voice.

(my translation; cf. also Erickson 1995, 17;

Ellsworth 1993, 165)

Clearly, the discussion and justification of why the diapason is "more perfect" is

based on the actual perception of sound (i.e., on sound itself), not on a speculative

justification by number. It is also evident that the diapason is considered just as consonant

as the unison itself, which it may even replace—the quotation above is followed by a

musical example of a three-voice parallel organum at the octave, as a perfect substitute for

the monophonic version of the chant, when sung at different voice-registers (in this case,

consisting of one childlike and two different adult male voices).67 In Hucbald's treatise (De

67 Note that already in this ninth-century treatise, the concept of change (mutation) from one

sound to another is already present, though it is mentioned within the polyphonic context of organum.

Notice, also, that in the translation "the voice ... you may have mutated according to the octave into a

loftier or humbler [voice]," the terms "loftier" and "humbler" are literal translation from "celsiorem" and

humiliorem ," which could also be translated as "higher" and "lower"—the latter translation is not employed,

85

harmonica institutione, ca. 900), the diapason is also explained in practical terms. His

approach is even more conspicuous with respect to the octave equivalence, in that it indicates

pairs of steps (first and eighth, second and ninth, etc.) in relation to the gamut that he had

presented earlier (one based on the Greater Perfect System).

Itaque prima cum octava, et secunda cum

nona, tertia cum decima, et ite per ordinem

singulae inferiores cum singulis superioribus

pulsae, dulci et concordabili suavitate

omnimodis consonabunt, ac si unus,

simplexque sit sonus: et haec talis concordia

diapason consonantia appellatur.

(Hucbald ca. 900; GS 1: 111; PL 132:

913–914)

Thus if the first note is sounded together

with the eighth, the second with the ninth,

the third with the tenth, and so, throughout

the range, individual lower notes are sounded

with the corresponding [singulis] upper

notes, they will blend with an altogether

pleasant and harmonious sweetness, as

though the sound were one and single. This

sort of concord is termed "the consonance of

the diapason."

(Babb 1978, 25)

Almost a century later, the anonymous (pseudo-Odonian) treatise entitled Musica

artis disciplina (from the late-tenth century) provided an approach not only related to

musica practica, but also including allegorical (and more adjectival) references, in order to

help the reader toward a more appropriate aural perception (and performance) of the

diapason and of its importance in relation to other musical elements.

Est autem in hac symphonia divinum, quod

prima vox eius et ultima tam mirabili

suavitate concordant, ut eamdem vocem una

This symphony (i.e., the interval of

diapason) is however divine, for the first and

the last voice (vox, i.e., sound) of this

since it could create some confusion with the already existing "on a higher or on a lower [place]," translated

from "ab acutiore sive a graviore." As for the translation "may be held [as]," for the verb "habeatur," a

more literal rendition could be given as "may have had," although it should be understood in the sense of

"may be handled [as]" or, even preferably, "may be considered"—thus providing the freer rendition "the

voice, which you may have mutated to the octave, may be considered a unison to the first voice" for the

sentence "vox, quam octavo ordine [...] mutaveris, ad primam vocem unisona habeatur."

86

atque altera sonare videantur; licet prima

virilis, et ultima sit puerilis: ita enim

concordant, ac si vir cum puero eandem

melodiam simili, quantum diversa natura

permittit, voce pronuntient.

(Pseudo-Odo ex. 10th cent. M; GS 1: 271;

PL 133: 780)

[symphony] agree so much in marvelous

pleasantness, that one and the other seem to

sound [as] the same voice; the first may be

manly and the other childlike. Thus they

indeed agree, as if a man with a boy sing

(voce pronuntient) the same melody, as far

as [their] diverse nature allows.

(my translation)

From the early to the late Middle Ages, and throughout the Renaissance (and even

after), theorists continuously and consistently assessed the merits and properties of the

octave (diapason), stating that, by its nature and proportion, it is an interval so consonant

that it may sound as one single sound, to a point that it even might be difficult to perceive

the distinction between its two formative sounds when performed simultaneously. In this

context, the anonymous author of the Musica artis disciplina treatise elaborated on the idea

that such a distinction resides in the different qualities of sound of one step and the other, or

more precisely, in the difference of timbres between the two steps—the higher being more

childlike, the lower more manly. This, in fact, accounts not only for a means of recognizing

that distinction, but also for the differences and means of producing the two sounds that

make up the octave.68 In the latter quotation (and in the other quotations above in this

section), although the context is one of intervals performed simultaneously, it also points,

68 In Musica enchiriadis (see above), the assessment-allegories of "loftier" and "humbler"

voice-production (respectively corresponding to the "higher" and "lower" steps) also attempt to provide

further understanding of the merits and properties of the diapason, but they share no direct correspondence

with those allegories provided in Musica artis disciplina. In a comparison between the two assessments,

their correspondence with respect to character or timbre (loftier corresponding to the adultlike voice, and

humbler to the childlike voice) is in contradiction to their correspondence with respect to pitch (higher

being loftier but childlike, and lower being humbler but adultlike).

87

implicitly, to understanding how an octave may be produced by one single voice. In terms

of octave equivalence, once the sound and step-syllable (from within the strict limits of the

hexachord) have been aurally imagined, it takes no more than a simple timbral change (or

timbral mutation) for the octave to be produced. Paraphrasing the author of Musica artis

disciplina, it could be thus stated: if one intends to sing the upper octave of any

hexachord-limited step, one will need to make a change toward a more childlike voice; and

conversely, if one intends to sing the lower octave, a change toward a more adultlike voice

should be made. This practical (performing) way of identifying and producing an octave

(whether melodically or polyphonically) was already present in theoretical discussions by

other authors, as can be clearly interpreted, in Boethius's treatise, from a passage on the

matter of comparing consonances and judging their hierarchical importance.

Quae consonantia quam merito praecedat.

XXXIII.

Sed inter omnes quas retulimus consonantias

habendum iudicium est, ut in aure, ita

quoque in ratione, quam earum meliorem

oporteat arbitrari. Eodem namque modo auris

afficitur sonis vel oculus aspectu, quo animi

iudicium numeris vel continua quantitate.

Proposito enim numero vel linea nihil est

facilius quam eius duplum oculo vel animo

contueri.

(Boethius a. 510; bk. 1, ch. 32; Friedlein

1867, 222; GB-Ctc R. 15.22 (944), f. 26r;

PL 63: 11194)

32. Which consonances precede others

in merit

Judgement should be exercised with respect

to all these consonances which we have

discussed [diapason, diapente,

diapason-plus-diapente, diatessaron,

diapason-plus-diatessaron, and bis-diapason];

one ought to decide by the reason, as well as

by the ear, which of them is the more

pleasing. For the ear is affected by sound or

the eye by a visible form, in the same way

the judgement of the mind is affected by

numbers or continuous quantity.

(Bower 1989, 49)

In other words, the recognition of consonances is made both by means of

philosophical speculation (i.e., "by the reason," "by numbers"), and by means of practice

88

(i.e., "by the ear," "by sound"). The importance of the diapason, however, does not lie only

in its status as the most perfect, or the most pleasing consonance, but also by its service as a

measuring unit or paradigm for the deduction of other intervals. Octave relations served, for

instance, as a basis for the construction of the gamut, through the monochord. In musica

speculativa treatises, the very first interval to be deduced is the diapason, by dividing the

string of the monochord into two equal parts. In musica practica treatises, even if the

monochordal divisions began with the tone, followed by a gradual, stepwise approach up to

the seventh above the open string, still the diapason was used as the main underlying

interval to support all intervallic deductions, and to obtain steps that otherwise would involve

too complex divisions (e.g., the other steps above the seventh were deduced by dividing the

string lengths of each step in half, thus obtaining their octaves, and also generating

compound intervals).69 Any performer was systematically exposed to octave equivalence

situations, that included but were in no way limited to primary learning situations. Students

may have been asked to find steps on the monochord, or they may have been asked to

deduce and organize hexachords according to family categories—for instance, by grouping

together the recta-hexachords of the durum family, including all -hexachords no matter if

they began on Γ-ut, or on G-sol-re-ut, or on g-sol-re-ut, thus grouped according to

'likeness' of sound (or even 'equalness,' but not 'sameness'). The task of the performer (as

the learning process of any student) most certainly involved some awareness of the sound

equivalences (especially that of the octave) in order to sing and solmize—a solmization in

69 Cf. Adkins (1963, 78–80; 1967, 39–41).

89

which the maintenance of the same hexachord, whenever possible, was regarded not only as

the easiest way for solmization, but as a rule of necessity. In historical treatises, instead of

providing statements that a hexachord should be maintained for as long as feasible, theorists

asserted rather that changes to another hexachord (i.e., mutations) should be avoided, unless

absolutely necessary—this is evident from the quotations given below.

Et sciendum est quod quantumcunque

possumus operari cantum per has voces

universales ad omnem musicam, scilicet ut,

re, mi, fa, sol, la, debemus mutationes

evitare et eas percavere, nisi possunt evitari

vel percaveri. Sed dum venerit necessitas

mutationem agendi, tunc debet fieri et non

aliter [...].

(Garlandia p. 1240; CS 1: 160)

And it must be known that as much as we

can perform (operari) the chant through these

universal voices (voces, i.e., syllables) in

every music, namely ut, re, mi , fa, sol, la,

we ought to avoid mutations, and beware of

them, unless they can[not] be avoided or be

kept away. But if only the necessity may

come for executing (agendi) a mutation, then

it ought to be made and not otherwise [...].

(my translation)

————————

Et nota quod non debet fieri mutatio nisi

causa necessitatis.

(Capuanus 1415; La Fage 1864, 315)

And notice that you must not make a

mutation unless because of necessity.

(my translation)

Both Garlandia and Nicolaus Capuanus, although almost two centuries apart,

maintain that holding to the solmization of one single hexachord is preferable, changing

only in the face of necessity. Octave equivalence is a concept (and a practice) that would

have allowed and implemented such a solmization, although this judgement appears to be

challenged in the statement of a later theorist (Johannes Cochlaeus).

Fit autem Mutatio triplici de causa. Primo

ad concipiendum suauioris modulationis

transitum: Ad quem saepe non minus facit,

A mutation is made for three reasons:

1. In order to make a more pleasant melodic

transition, in which the quality of a tone is

90

variata vocum qualitas, quam permutata soni

modulati quantitas. Secundo vt infra et supra

vnumquodque Hexachordum voces liceat

intendi et remitti. Tertio ad faciliorem

Diatesseron ac Diapente transitum in

tonorum permixtione, Nam quilibet tonus

octauam regulariter continet. ad quam absque

mutatione non pertingitur.

(Cochlaeus 1511–14, tr. 2, ch. 8, f. B vv)

changed no less frequently than the size of

the tone.

2. To permit tones to go above and below a

hexachord.

3. To facilitate the exchange of a fourth and

a fifth in a mixture of Tones, for each Tone

normally comprises an octave [, which is

not reached without mutation.]

(Miller 1970, 42)

(The last phrase in the translation is enclosed in brackets, since it has not been

included in Miller's version.) By stating that "an octave [...] is not reached without

mutation," Cochlaeus may appear to be saying that an octave-leap cannot be sung with one

and the same hexachordal syllable. However, he is neither referring to any kind of leap, nor

to any kind of melodic motion. Cochlaeus is merely saying that the full span of a mode

(i.e., "tone" in Miller's translation) can be covered (or solmized) only if some kind of

mutation occurs either on the fourth or on the fifth, because a mode is defined (at least since

the early Ars Nova) as a conjunction between a diapente and a diatessaron, or vice versa

(depending on whether it is authentic or plagal). Cochlaeus's third reason for mutation

could be thus paraphrased: 'Since each mode normally comprises an octave, a mutation is

needed at the point where the diatessaron meets the diapente, for that octave cannot be fully

covered [in stepwise motion] unless by means of mutation; therefore when there is a

mixture of tones, a mutation will also be needed.'

A few decades after Cochlaeus's treatise, Hermann Finck (Practica musica, 1556)

provided an explicit support to the above claims of octave equivalence in the sixth of nine

"rules of solmization."

91

Mutatio uocis non semper fit in uocem, sed

fit saltus sine mutatione de nota ad notam,

praesertim in magnis saltibus, ut in diapente

et diapason contingit, scilicet: de re in re, ex

mi in mi, de fa in fa, ex sol in sol.

(Finck 1556, bk. 1, f. F ir)

Mutation of a syllable is not always made

on the [same] syllable, except [when] a leap

is made without mutation from note to note,

especially in large leaps, as it happens in the

[leaps of] diapente and diapason, namely:

from re to re, from mi to mi , from fa to

fa, from sol to sol.

(my translation)

In the next section of his treatise, Finck also addressed the need for mutation,

proceeding from the same line of thought that gave rise to Garlandia's and Nicolaus

Capuanus.

[...] uocum mutatio non debet fieri praeter

necessitatem.

(Fink 1556, bk. 1, f. F iv)

[...] the mutation of a syllable (vox) must

not be done except for necessity.

(my translation)

Still later in the treatise, in the section dedicated to solmization, Finck emphasizes the

concept of octave equivalence in his "rules of solmization" (quoted below is his fourth and

last rule).

In octauis idem est uocum usus, et eadem

mutatio: Ideoque quaecunque uox canitur in

una octaua, canitur et in alia.

(Finck 1556, bk.1, f. F ijr)

The same syllable (vox) is used at the

octave, and the same mutation; and therefore

whatever syllable is sung at one octave, is

also sung at the other.

(my translation)

Here, the author clearly states that when one hexachord is used at one octave, it may also be

used at another, and therefore mutation is virtually nonexistent in this case.

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(v) Refutation: Resistance to Hexachordal Solmization

The Guidonian paradigm of hexachordal structures was doubtless the most

influential and accepted frame for solmization, lasting at least to the end of the Renaissance,

as attested in a quotation (given below) from the watershed work of Gioseffo Zarlino (Le

istitutione harmoniche, 1558).70

Imperoche Guidone Aretino nel suo

Introduttorio, oltra le nominate chorde, ve ne

aggiunse delle altre alla somma di Ventidue,

et le ordinò in sette Essachordi; et tale

ordinatione fu, et è più che mai accettata, et

abbracciata dalla maggior parte de i Musici

prattici: essendo che in essa sono collocate,

et ordinate le chorde al modo delle mostrate

Pithagorice.

(Zarlino 1558, pt. 2, ch. 30, p. 103)

Thus Guido d'Arezzo in his Introduction,

more than having nominated the strings

(chorde, i.e., steps), appended others to

[reach] the total of twenty-two, and arranged

them in seven hexachords. And such an

arrangement was, and [still] is

overwhelmingly accepted, and embraced by

the majority of the practical musicians; so

that, in it, the steps are placed and arranged

according to the way demonstrated by the

Pythagoreans.

(my translation)

Despite the widespread acceptance of Guidonian solmization and its hexachords,

there were a few theorists who opposed the monopoly held by that method. Johannes

Ciconia (ca. 1370–1412) was one of those who criticized (subtly but utterly) the

"Guidonists" and the use of the Guidonian "hand" (i.e., of hexachordal syllables) while

defending that, instead, the letters marked on the monochord should be preferably used for

solmization. Naturally, Ciconia did not declare that the Guidonian paradigm had no use, nor

70 Despite Zarlino's assertion, there is no evidence that Guido extended the gamut to twenty-two

steps, which would necessarily include ee (a step he never seems to have used), as well as and (steps

not consistently included in all of his treatises)—cf. (Babb 1978, 52; Pesce 1999, 25–29).

93

did he challenge Guido's authority (from whose treatises, especially the Micrologus and the

Epistola, he provided many quotations to support his explanations about intervals, organum,

and modes). Nevertheless, Ciconia did attack the so-called "ignorance of the Guidonists"

("ignorantia Guidonistrarum"), which he hoped would cease in face of the alleged proof he

provided in his treatise, and that he hoped would not prevent the appropriate understanding

of the material he was exposing.71 In Ciconia's assertions, given below, it appears that the

"Guidonists" are those who have ill-comprehended and ill-applied the Guidonian teachings

without proper knowledge of what previous authorities had taught, and without proper

modern instruction about those and other paradigms.72

31. De addiscendo cantu

Si quis cantum musice scire cupit, primum

quidem investigare opportet in monocordo et

in cantu positionem ordinem et figuras

septem litterarum gravium, acutarum, et

31. On learning to sing

If one whishes to know a song of music, it

is necessary first to find—on the monochord

and in the song—the position, arrangement,

and the symbols of the seven graves, acutae,

71 Cf. Ciconia (ca. 1400, bk. 1, chs. 20, 59, 60; Ellsworth 1993, 88–89, 210–211, 216–217).

72 In a footnote to the term "Guidonists," Ellsworth provides the following interpretation:

It is not possible to identify precisely these followers of Guido—the "Guidonists." Ciconia's later

references to this group (see 1.59, 1.60, and 2.31 [pp. 208–9, 214–17, 302–5]) do indeed appear in

connection with material that can be located in the known works of Guido, but the reference here is

too vague to allow such a direct connection with Guido.

(Ellsworth 1993, 89n)

Also, Ellsworth calls attention to the fact that Guido "is the latest of the early authors cited by

Ciconia" (Ellsworth 1993, 16), with Boethius, Isidorus Hispalensis, Remigius Autissiodorensis, and Berno

Augiensis receiving a greater number of citations. Later theorists, explicitly cited, include Franco de

Colonia, Hieronymus de Moravia, Johannes de Muris, Marchettus da Padova, but no other between these

and Guido d'Arezzo are mentioned by Ciconia—cf. (Ellsworth 1993, 13–20).

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superacutarum, que sunt in lineis et in

superlineis cum ordinatis coloribus suis.

Deinde coniunctiones vocum. Post hec

unum e duobus eligat. Aut computum, ut

Guidoniste, aut monocordum, qui numquam

fallit, ut bonus magister. Ad hoc etiam

cantus consonantiarum et specierum

maximum prestant intellectum. Igitur,

prudens lector, post agnitionem litterarum et

vocum coniunctiones modo in computum,

modo in monocordum, modo in cantus

consonantiarum et specierum operam det, ita

ut ab exercitio numquam cesset, donec

ignotos cantus ut notos suaviter cantet, ut

Guido refert.

(Ciconia ca. 1400, bk. 2, ch. 31; Ellsworth

1993, 302, 304)

and superacutae letters that are on the lines

and additional lines, with their prescribed

colors; then, the conjunctions of pitches.

After this, one should select one of two

things; either the hand, like the Guidonists,

or the monochord, which, like a good teach-

er, never misleads. An understanding of the

consonances and species will also be most

important for this song. Therefore, prudent

reader, after the recognition of the letters and

the conjunctions of pitches—whether on the

hand, the monochord, or the consonances and

species of songs—one should work so that

he never ceases to practice until he may

pleasantly sing unknown songs like known

ones, as Guido reports.

(Ellsworth 1993, 303, 305)

Despite his animosity toward the Guidonists, Ciconia did state in the passage above

that the student can choose between three methods of proper solmization in learning a new

chant: the monochord, Guidonian solmization syllables (via "the hand"), and active

application of consonances and their species. In this context, he called on Guido's authority

to assert that most importantly a solmization method needs to be practiced long and

diligently in order to be effective, a justification for his idea that virtually any method will be

suitable for solmization. However, he also explicitly states his resistance to Guidonian

solmization, by saying that "the Guidonian hand" can be a faulty, misleading method, and

that the monochord is (and in his opinion should always be preferred as) a better

substitute.73 In Ciconia's case, this resistance was a sign of a humanistic trend to undertake

73 These and the following considerations about Johannes Ciconia's opinions are indebted to a

paper delivered, at the AMS Annual Meeting in 1998, by Stefano Mengozzi, who kindly granted me a

copy. His main object was to discuss what he identified as "those 'pockets of resistance' against Guidonian

solmization" (Mengozzi 1998, 1) throughout the Renaissance, and particularly in the work of Ciconia.

95

a "renovatio antiquitatis," i.e., theorizing and explaining music based on reinterpretation of

authors from Classical Antiquity and early Middle Ages, while emphasizing the

misapprehension embedded in works of some late-medieval authors.74 Nevertheless, the

prominence of the Guidonian hexachordal solmization can hardly be denied, and the

partiality of such a resistance becomes evident if one considers that it may have been arisen

from a conflict between Germanic trends that emphasized theoretical (musica speculativa)

concerns, and Italian-influenced trends of a more practical nature.75 By placing an

emphasis on solmization of steps derived directly from the monochord, Ciconia was

seemingly vouching for an approach that, instead of being restricted to the span of the

hexachord, was founded on octave arrangements (for this was the basis for obtaining and

marking steps in the monochord), i.e., produced by an entirely different way of step

recognition, which eventually contributed to forward the modern concept of pitch as a fixed,

individual, and independent entity.

Johannes Hothby (ca. 1430–1487) also presented a different concept regarding

solmization and organization of the Gamut (apparently attempting to unify Guidonian and

Pythagorean traditions), which has been seen as a potential anticipation of the modern

74 Cf. Tatarkiewicz (1970, 3: 32–36).

75 The latter consideration is drawn from commentaries formulated by Peter M. Lefferts and

Oliver B. Ellsworth, as responses to Mengozzi's lecture at the AMS-1998 session mentioned above.

Lefferts commented that the probable Germanic background of Ciconia's work may have influenced his

criticism toward Guidonian solmization (and therefore toward the use of the Guidonian hand), and

consequent reliance on the monochord as a more appropriate device for solmization.

96

concept of accidentals (which is also related to the modern concept of pitch).76 He

identified three different orders of hexachords (all based on Guidonian solmization

syllables): the first order containing only - and -hexachords and all the correspondent

steps (i.e., virtually equivalent to the steps of recta-gamut, but excluding -fa or any of its

possible octaves); the second order containing hexachords in which the syllable fa is applied

where it is not found in the first order; and the third order containing hexachords in which

the syllable mi is applied where it is not found in the first order—both the second and third

orders also include the - and -hexachords that represent the first order.77

Ramos de Pareja's Musica practica (1482) may also be identified as an example of

the resistance to Guidonian-based solmization, especially with regard to the use of

76 These considerations about J. Hothby are based on the survey provided by Bonnie Blackburn

(NG 2e, s.v. 'Hothby, Johannes'), and on a paper entitled "John Hothby—Innovator: The Solmization

System of La Calliopea legale" presented at the New England Conference of Music Theorists 19th Annual

Meeting (Boston, 2004) by Sigrun Heinzelmann—cf. also (Seay 1955, 86–92; Berger 1987, 21, 36–37).

77 In establishing the internal semitone, Hothby had also made an allegorical classification of the

steps, with regard to their surrounding intervals (i.e., a classification that considered their relation to

surrounding steps). A step that established a semitone above and a whole tone below should be named a

principe (i.e., prince), and conversely a step that had a whole tone above and a semitone below should be

named a comite (i.e., count)—thus, the mi syllable was the principe, and the fa syllable was the comite.

(Each of the other steps, which had a whole tone above and another below, should be named

demonstratore—i.e., demonstrator.) This classification sets a clear necessity for understanding Hothby's

presentation in light of societal and political relations. Hothby was apparently working in Florence, before

he assumed a post at the competing city of Lucca in 1467, where he basically spent the rest of his life—cf.

(Seay 1956). The Republic of Lucca had its own share of political and societal issues, having its northern

boundary with the Duchy of Modena (in the hand of the Estes), and the other boundaries (south, east and

west, despite a narrow western escape to the sea) with the powerful Republic of Florence (in the hand of the

Medicis). The regional context of power may have had an influence (which remains to be investigated) on

Hothby's allegories and musical works, as much as it had an unquestionable influence on the production of

contemporaneous political works—like those of Niccolò Machiavelli (1496–1527), even if his output is

dated from the beginning of the sixteenth century.

97

hexachords and mutation, that were necessary to make the system work. Ramos de Pareja

proposed an eight-syllable set for solmization (psal-li-tur per vo-ces is-tas) that was

constructed upon a stepwise scale from C to c (or, in modern pitch equivalents, from c to c').

Like the modern fixed-do system, Ramos de Pareja's set would not use different syllables

when step alterations or varieties were intended: e.g., although his basic gamut did not

include the b–rotundum, that step-letter could occur when needed, but it would still be

solmized with the same syllable "is" that served for the b-quadratum. Apparently, one of

Ramos de Pareja's purposes was to avoid or perhaps eliminate the need for hexachordal

mutation. Thus, he too may be counted among that group of theorists whose propositions

are interpreted as anticipations of the modern concepts of pitch and accidentals. In a chapter

entitled "Reproaching the followers of Guido and accurately demonstrating the thruth of

things" ("Reprobans Guidonis sequaces et veritatem rei subtiliter demonstrans"), Ramos

de Pareja additionally refers to the work of Johannes Gallicus (ca. 1415–1473) as one of

the sources (and justification) for his own propositions.

Bene quidem dixit de his mutationibus ipse

frater Johannes Carthusinus: non dico vocis

in vocem mutationem, sed ab ambage in

ambagem variationem. Solum refert tonos et

semitonia annotare et per litteras Gregorii

canere. Hoc equidem de vocibus meis dico.

(Ramos de Pareja 1482, pt. 1, tr. 2, ch. 7,

f. 18r; cf. Wolf 1901, 44]

Brother Johannes the Carthusian, spoke

indeed well of these mutations: "I do not say

a mutation from syllable to syllable, but a

variation from ambages to ambages. It is of

importance only to notate the tones and

semitones, and to sing by means of the

Gregorian letters." Indeed, I say this about

my own syllables.

(my translation; cf. Henderson 1969, 298;

Miller 1993, 94–95)

It is noticeable that Ramos de Pareja is attempting to emphasize that one can solmize

98

a piece of music without the aid of mutation (i.e., change), and stresses (following Gallicus)

that 'mutation' is akin to 'ambages' (also spelled 'ambage'), a rhetorical figure also known by

the name 'circumlocution.'78 'Circumlocution' (or 'ambages') refers to an idea, thing, or

image, that can be implemented in three different ways: by means of 'euphemismus,' by

means of successive rephrasings, by means of more or less literal restatements.79 The

implementation by means of euphemismus is the most commonly accepted form of

circumlocution, and involves a reference to a subject in some other form than saying it

directly, usually to avoid discourteous, unlearned, or even vulgar meanings—e.g., the 'fear of

being sexually violated by some unknown person' might be poetically mentioned as 'the

78 The same passage from Ramos de Pareja's treatise is quoted in Henderson's dissertation, where

he mentions that "Gallicus' references are in Edmond H. Coussemaker, Scriptorum, IV, 347, 349, 374"

(Henderson 1969, 298), and interprets that Gallicus's quotation runs from "non dico" to "Gregorii canere"—I

could not find the latter part of the quoted passage ("Solum [...] Gregorii canere") in Coussemaker's edition

(CS 4: 349, 374), as Henderson suggested. In Miller's translation, he also understands that Gallicus's

quotation runs from "non dico" to "Gregorii canere," but gives the following reference with regard to

Gallicus's text: "Coussemaker Scriptorum IV, 347b. See J. Gallicus, Ritus canendi, ed. A. Seay, II, p. 3,

note 21: non dico, vocis in vocem mutationem, sed ab ambage in ambagem; p. 4, note 23: Idcirco notae

quadrae quibus nunc utimur nihil praeter illas septem repraesentant litteras A C D E F G" (Miller 1993,

94n). Thus, Ramos de Pareja's assertion qualifies more as paraphrase based on the second part of Gallicus's

statements, than as a literal quotation. Even in the first part ("non dico [...] variationem"), Ramos de

Pareja alters Gallicus's original: "non dico, vocis in vocem, sed ambagis in ambagem mutationes [...]

atterere" ("I do not say to weaken the mutations from syllable into syllable, but from ambages into

ambages"—cf. (Gallicus 1458/64, pt. 2, bk. 1; CS 4: 347; Seay 1981b, 14: 3).

79 In modern English studies of rhetoric, George Puttenham (ca. 1520–1590) is frequently

mentioned as the rhetorician who applied the term 'ambage' for 'circumlocution' in his The Arte of English

Poesie (1589). Despite this attribution, the feminine noun 'ambages, -is' already existed in Latin, and some

of its meanings (all of which may also serve for the plural noun 'ambages' in English) were: ambiguity,

double-talk, digression, lie, roundabout way, circuitous paths, mysterious ways—the connection with the

figure of rhetoric called 'circumlocution' is rather obvious.

99

robbing of one's treasure chest by a ruthless thief in the middle of a dark night.'80 The

implementation by means of successive rephrasings is generally used to emphasize the

subject under consideration, and is also usually derived from the euphemismus—it simply

restates the same subject several times, each one with a different euphemismus. The third

implementation, by means of literal repetitions, is commonly taken as a rhetorical vice, since

it involves a tentative explanation of a subject simply by repeating its main words, therefore

producing no real explanation—as in the phrase: 'a two-voice strict parallel organum is

defined as a piece of music in which two voices proceed in parallel movement to each other.'

This latter type of circumlocution is usually not mentioned in rhetoric methods because it is

virtually unacceptable and unusable. Ramos de Pareja's text can be interpreted in this

context. His intention is to provide solmization with a conspicuous, clear understanding of

the intervals (whose best indication would be his own set of syllables, with one exclusive

syllable per step), and so he suggests that any procedure that would prevent the true

understanding of the intervals is unacceptable and unusable. The Guidonian paradigm (with

its non-exclusive syllables) is thus identified as circumlocution ("ambages"), for its

immanent process of mutation could suggest ambiguity, since a sound can be uttered by two

or more syllables pertaining to different hexachordal structures—even when it is an

80 Cf. G. Burton (1996–2004, s.v. 'circumlocution').

100

expansion of meaning, as with any of the euphemistic approaches. His innovation

notwithstanding, Ramos de Pareja's propositions had no effect on actual solmization.81

The evidence provided in Ramos de Pareja's treatise suggests that Johannes Gallicus

may also have had in mind some kind of resistance to Guidonian solmization. In his

interpretation of Gallicus, however, Ramos de Pareja cited only understandings that could

support his own propositions. Gallicus did indeed address Guido's hexachordal

propositions, and speculated both about its origin and its application, but he was hardly

proposing any substitutes for Guidonian solmization.

[...] quaerendum est cur Guido novam illam

introducere volens canendi formam sex solas

syllabas elegerit, et non potius quindecim

iuxta numerum ordinis philosophorum, aut

tot quot voces communis sui temporis usus

habebat, seu quatuor duntaxat aut plus aut

minus. Ad quod respondendum breviter,

quoniam musicus erat et non cantor purus,

non nesciens omne quod canitur, quatuor

tantum concludi vocibus ac duobus cum

[...] one must examine why Guido, wanting

to introduce that new form of singing,

elected only six syllables, rather than fifteen

according [to] the number of the

philosophical order, or else as many voices

as was the common use of his time, or only

four, or else more, or else less. Answering

briefly to that, since he was a musician and

not a pure singer, [and] not ignoring all that

was sung, he perceived (concludi) only four

81 Robert Henderson gives the following assessment about Ramos de Pareja's new set of

syllables:

Ramos' syllables were not put to any practical use, Ramos himself uses Guidonian syllables to

illustrate many of the points in his book. Why was there no acceptance? Most probably, the

syllables were too new. They had nothing in common with the older, highly popular Guidonian

solmization. On the other hand, they offered no advantage over the alphabetical pitch letters to

which they were attached.

(Henderson 1969, 298)

Henderson's dissertation is one of the first works to interpret and call attention to the passage

(quoted above) and other references from Ramos de Pareja's Musica practica, and from Johannes Gallicus's

Ritus canendi, as signs of opposition to the Guidonian paradigm of solmization.

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semitonio minori tonis, quod totum aut

prima consonantia diatessaron ab antiquis

philosophis appellatur aut tetracordum, hoc

est, quatuor cordarum. [...].

Nimirum necesse fuit Guidonem, cuius

propositum erat, quam breviter totum

exprimere cantum has sex nec plus nec

minus aut alias huiusmodi totidem fabricare

syllabas. Quis enim nesciat per ba, be, bi,

bo, bu, bam, id fieri potuisse, vel per aliud

quippiam simile? Quicquid etenim canendo

proferre velis, observa tonum et

semitonium, et optimum erit?

(Gallicus 1458/64, pt. 2, bk. 2; CS 4: 375;

Seay 1981b, 14: 51–52)

[syllables] from the voices and in two tones

with a minor semitone, for the whole or first

consonance [which] was called diatessaron or

tetrachord by ancient philosophers, that is,

of four strings. [...].

Surely, it was necessary for Guido (whose

purpose was to describe [exprimere] all chant

as briefly as possible) to forge these six

syllables, neither more nor less, nor others

of this kind with the same [number]. For

instance, who does not know that it could be

done by way of [the syllables] ba, be, bi, bo,

bum, bam, or by way of any similar others?

(my translation; cf. Henderson 1969, 19–20)

In his assessments, Gallicus does seem to refute hexachordal solmization as too

verbose (in as in his use of the term 'ambages'), and appears to be momentarily in favor of a

solmization based on the tetrachord. He understands that the tetrachord represents the

origin of musical speculation, and even identifies the tetrachord as the structure that spells

out the most important consonance for singing (the diatessaron). But by the end of the

quotation, when Gallicus suggests that one could even use a different syllable-set of six

syllables, he is actually attesting to the appropriateness of Guido's choice. In his phrasing,

Gallicus also implies that the exact set of syllables has virtually no importance, for everyone

knows (according to his claim) that it could be done by way of any syllable-set, even one of

a babbling character such as ba, be, bi, bo, bum, bam.82 In another section of his work,

Gallicus presented a diagram introduced by the following words: "Haec docet figura

82 For a survey and analysis of these and other sets of solmization syllables, see Henderson

(1969, 259–301); some of the sets he discusses involve four syllables, others seven, and even others eight

syllables. Henderson, however, interprets Gallicus's assessments as a resistance to Guidonian solmization.

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modulari per litteras breviter ac faciliter et per ut, re, mi, fa, sol, la" ("This figure teaches

how to sing briefly and easily through the letters and through ut, re, mi, fa, sol, la"). (In the

quotation of the diagram, below, the letter "T" stands for "Tonus" in Gallicus's original, the

uppercase "S" stands for "Semit[onium] maj[oris]," and the lowercase "s" stands for

"Semit[onium] min[oris].")83

TABLE I – Gallicus's solmization for the entire gamut

Haec docet figura modulari per litteras breviter ac faciliter et per

ut, re, mi, fa, sol, la

Tonus Tonus

T T s T T s T T s S s T T s T T s S s T T

Γ A C D E F G A C D E F G A C D E

UT RE MI FA SOL LA FA SOL LA FA MI FA SOL LA FA SOL LA FA MI FA SOL LA

(Gallicus 1458/64, pt. 2, bk. 2; CS 4: 377; Seay 1981b, 14: 56)

The diagram is a representation of the entire gamut, from Γ to ee (including both

and ), but showing only one syllable per step-letter (all based on the Guidonian

hexachord). A possible interpretation is that the diagram shows a gamut in which no

mutations would be necessary, since only one solmization syllable is assigned to each step.

There is no doubt that Gallicus, in his engagement with humanistic trends, had reservations

about Guidonian-influenced solmization, as much as about Marchettus da Padova's work,

83 In Coussemaker's edition, the last (higher) "Semitonium" is given as "maj[oris]," but it has

been corrected to "s" (i.e., "Semitonium minoris") in Seay's edition. The phrase that introduces the

diagram, in Seay's edition, is given with only a minor variant: "Haec docet praesto figura Modulari per

litteras Breviter ac faciliter Et per ut, re, mi, fa, sol, la" (Seay 1981b, 14: 56; underline mine).

103

although he was (perhaps paradoxically) also regarded as a conservative theorist. But a

close reading of Gallicus's text will indicated that the diagram was neither a proposition to

forge fixed-pitch syllables, nor an attempt to eliminate the need for mutation, although it

seems reasonable that the diagram might have been based on the precept that 'mutation must

not be made unless because of necessity'—therefore apparently enabling steps to be

solmized only by means of that one syllable.84 In fact, the figure served merely as a

simplified diagram of the gamut, in which Gallicus suggests how to identify (represent) the

entire gamut, by means of an uninterrupted sequence of syllables, in a stepwise, brief and

easy manner ("breviter ac faciliter"), which is still indebted (and must still adhere) to the

Guidonian paradigm. Thus, the solmization of the diagram is confined mainly to mutations

between the - and -hexachords, while the presence of -fas accounted for momentary

-hexachord steps, apparently effected in fa-super-la circumstances.85 Gallicus seems to

attest that, a priori, solmization should predominantly use the - and -hexachords, except

for momentary situations that call for the use of the -hexachord in order to provide the step

-fa, or unless specified otherwise. In that sequence of syllables one particular species of

the diatessaron is emphasized (s-T-T, thus solmized mi, fa, sol, la), which serves as the

84 Cf. Gallicus (1458/64, pt. 2, bk. 2; CS 4: 376–382; Seay 1981, 14: 53–62). The precept

mentioned above is a rephrasing of the following assertion by Nicolaus Capuanus: "And notice that you

must not make a mutation unless because of necessity" ("Et nota quod non debet fieri mutatio nisi causa

necessitatis")—cf. (Capuanus 1415; La Fage 1864, 315).

85 The expression fa-super-la stands as a short form of the saying 'una nota super la, semper est

canendum fa' ('one note above la, must always be sung as fa'), or similar situations—which shall be

discussed in chapter 5 .

104

main structure underlying the entire gamut representation by Gallicus. In this sense, the

syllables demonstrate how to solmize through the entire gamut and imply what the

appropriate places for mutation are; e.g., in order to sing through the first F, which presents

the syllable fa, one needs to aurally conceive the syllable mi on the previous E, while it is

actually being uttered with the syllable la, and so, mutations should happen whenever the

hexachord reaches its final syllable la.86

Although the resistance to the Guidonian paradigm has been linked to humanist

trends of the Renaissance, it is worth noting that hexachordal solmization practice continued

at least until the first half of the eighteenth century, even if promoted only through

conservative pedagogical practices, and especially in relation to ecclesiastical singing. There

is, for instance, a report showing that during the years 1734–38 some musicians had

engaged in an interpretive dispute upon the viability of having key-signatures with seven

flats or seven sharps. Among the arguments against it, the contenders specifically

mentioned the (still current) practice of hexachordal solmization. The dispute, which gave

rise to wagers involving large amounts of money, actually reflected other contemporaneous

discussions on the necessity for different forms of temperament (i.e., tuning). Even if

restricted to a small group of Kapellmeisters who worked at the edge of the so-called

mainstream of Western-European musical practices and theoretical studies (since they were

mainly of Portuguese and Brazilian origin), its placement well within the period of J.S.

86 Henderson has misinterpreted this diagram, asserting that it represents a tentative elimination

of mutation, through the use of a non-mutating solmization system based on a four-syllable set—cf.

(Henderson 1969, 259–263).

105

Bach's composition of Das wohltemperirte Clavier (1722 [vol. 1], 1738–1740 [vol. 2] and

Jean-Philippe Rameau's Traité de l'harmonie (1722) is striking. The documentation of the

dispute was originally compiled and intended for publication in 1760 by the Brazilian Padre

named Caetano de Melo de Jesus (fl. 1734–1360), one of the contenders, and the one who

actually initiated the dispute; apparently, however, it was not published in his lifetime.87

Earlier indicators of resistance to Guidonian solmization might be interpreted from

treatises that did not take the Guidonian propositions, or their later expansions, as a

foundation for their theoretical discussions. Among those, two twelfth-century Cistercian

treatises may be cited: Guido Augensis's Regulae de arte musica (ca. 1140), and the

anonymous Tractatus Cantum quem Cisterciensis (1142/47). The former is a theoretical

treatise that was apparently used as a basis for musical learning in various chapters of the

Cistercian order. The latter treatise is, in fact, a preface to a Cistercian antiphonary, revised

and corrected under the direction of St. Bernard of Clairvaux (1090–1153). Both treatises

make no reference to Guidonian or to any definitive kind of solmization, although they seem

to allow the tetrachord as a possible device for solmization, the latter treatise providing a

short reference to the noeanne/noeagis set, mentioned as a way of deciding which is the

mode of a chant.

Ad hos inter se distinguendos, neumata

inventa sunt, singulis subiicienda

In order to distinguish these modes from

87 The first publication of that dispute has appeared only recently, under the title Discurso

Apologético: Polémica Musical, edited by José Augusto Alegria ([Lisbon]: Fundação Calouste Gulbenkian,

1985).

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antiphonis, quae apud quosdam stivae

vocantur, et apud Graecos signantur per haec

verba, nona, noe, ane, et noe ais, et his

similia, quae quidem nihil significant, sed ad

hoc tantum ab ipsis Graecis sunt reperta ut

per eorum diversos ac dissimiles sonos

tonorum admiranda varietas aure simul et

mente posset comprehendi.

(Anon. Cist. ca. 1147; Guentner 1974, 37)

each other, neumas have been devised to be

placed under each antiphon; by some these

are called stivae, and among the Greeks they

are designated by the words Nona, noe, ane,

and noe ais, and others similar to these.

These have no meaning, of course, but they

were formulated by the Greeks themselves

for the one purpose only, that through their

contrary and unlike sounds, the wonderful

variety of the modes could be perceived at

the same time by ear and mind.

(Guentner 1974, 56–57)

In fact, many twelfth-century treatises offered presentations that did not

acknowledge Guido's propositions in general, let alone follow the solmization system he

envisioned. However, such omissions of the Guidonian hexachordal paradigm (or any of

its syllables) can hardly be taken as a definite sign of resistance to the system since Guido's

propositions were still in the process of acceptance and practice. At the same time, it clearly

demonstrates that early theorists (at least in the twelfth century) did not always consider

following Guido as auctoritas for their discussions, and even when they did the

hexachordal paradigm would still take a little longer to be adopted as a norm.88

(vi) Working beyond the limits of the hexachord

88 In the quotation above, the plural noun "stivae" can be translated as "plough-handles." It

establishes a metaphor clearly intended as a suggestion of what the author considers to be the proper

character of those "neumas": the guiding force that underlies the identification and understanding of a

mode—i.e., much in the same way used by Guido d'Arezzo (melodic formulae or melodic gestures that

provide identification of a modes, and also of hexachords).

107

In the previous sections of this chapter, a method of recognizing individual

hexachords by means of melodic gestures was proposed, based on intervallic spans that

would signal the appropriate hexachord to be solmized. Frequently, however, when the

melodic context is extended beyond the limits of those strict intervallic spans, there is a need

for a change from one hexachord to another. In medieval and Renaissance theory, three

procedures of change can be identified: by mutation, by permutation, and by

transmutation.89

The first type of procedure, known as 'mutation' (from the Latin 'mutatio'), takes

place on a note that is common to both hexachords; i.e., the common mutation-step acts as a

link between two different hexachords being solmized. In this kind of change, the reading

of the chosen note would be generally done by thinking of a syllable according to one

hexachord, while saying (uttering) the syllable of the other hexachord. This procedure is

clearly similar to the modern concept of harmonic modulation, in which a chord common to

both keys is used as a link between them. At that point in which it serves a modulatory

function, the chord may receive a dual label: one according to the first key, and the other

according to the new key.

The second procedure of hexachordal change is known as 'permutation' (from the

Latin 'permutatio'), and could be explained as a transition that takes place on two different

steps that do not produce a common sound. Different from 'mutation,' 'permutation' was not

89 Additionally, the latter procedure (transmutation) may also happen even when there is no

apparent hexachordal change dictated by the melodic gesture, but when there is a need to avoid tritones, or to

create specific intervals in keeping with tradition, style, or voice-leading needs.

108

widely discussed, and a more precise formulation of its concept seems linked to various

attempts to clarify old concepts, as well as to tentatively define new musical propositions

brought forth by the humanistic ideals that were beginning to take shape in the

early-fourteenth century. Marchettus da Padova, in his Lucidarium (1317/18), seems to

have been the first author to explicitly enunciate the procedure of 'permutation,' although it

had clearly been in use at earlier dates. 'Permutation' may occur, for instance, when we meet

two steps in the same place (line or space) in the staff, but one is being solmized fa, while

the other will be solmized mi—e.g., 3-fa (b3) immediately followed by 5-mi (b5), or

vice versa. In this situation, 'permutation' can be described as a chromatic change (in

modern terms); since no single hexachord contains steps establishing such an inflection

between them, a change from one hexachord to another is unequivocally necessary.

The third procedure of change is being introduced in this dissertation under the

name 'transmutation,' which will serve as an indication of a momentary hexachordal change,

and, in relation to all three procedures, is the closest to today's concept of 'accidental

inflection'—although not all situations that call for a 'transmutation' will translate into

modern accidentals. A 'transmutation' generally occurs in a sequence involving at least three

different steps (i.e., disregarding consecutive melodic unisons), for which two alternative

approaches of solmization may be considered: (a) either the steps are all solmized according

to an extraneous hexachord (i.e., extraneous with regard to the whole gesture in which they

are included); or (b) only the second (middle) step is solmized according to an extraneous

hexachord, while the solmization of both its preceding and succeeding steps follows the

109

hexachord of the prevailing gesture. A 'transmutation' will occur most often when that

middle step can be identified as an upper neighbor-note, or as a subsemitone, or due to a

'propinquity' inflection.

The following chapters will present these three procedures individually: 'mutation'

will be discussed in chapter 3 (dealing with basic concepts, cases, and processes) and

chapter 4 (dealing with a more detailed analysis of its types and species); 'permutation' will

be discussed in chapter 5; and 'transmutation' will be covered in chapter 6. In an attempt to

interpret possible concealed meanings behind these procedures (which performers,

composers, scribes, and theorists are likely to have understood), chapter 7 will approach

them within a rhetorical context, tracing individual parallels with figures of rhetoric.

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— CHAPTER 3 —

MUTATION: THE BASICS

(i) Mutation (basic concepts)

The term mutation is a literal translation from the Latin mutatio, whose meanings

range from 'change' and 'exchange,' to 'transformation,' 'modification,' and 'shift,' among

others. In the context of Guidonian solmization, both in medieval and Renaissance theory,

the Latin word mutatio denoted a transition between two different hexachords. This

transition was generally necessary and inevitable, for it was determined either by melodic

gestures denoting different hexachords, or by ficta-signs imposing a different hexachord.

Consistent use of the term mutatio, in this context and meaning, appears only from the

thirteenth century onward, although analogous versions must have been employed in

pre-Guidonian solmizations, whether hexachordal or tetrachordal.90 Also, the concept of

90 For instance, changes similar to 'mutation' in the Guidonian sense may have happened in a

solmization of transposed modes based on the noeanne/noeagis set, or in solmizations intended to correct

dissonances derived from the Daseian notation—cf. (Anon. SE a. 900, pt. 1; GS 1: 175–177; PL 132:

984–988; Schmid 1981, 65–72; [trans.] Erickson 1995, 37–42). Other references may also be found in

Raymond Erickson's preface to the translation of Musica and Scolica enchiriadis (1995, xxxivn, xln, 8n),

and on Charles Atkinson's article "From 'Vitium' to 'Tonus acquisitus,'" in Cantus Planus (1990, 181–197).

111

mutation must have been derived from foundations of a more philosophical nature, as

Franchinus Gaffurius has mentioned in his Practica musice.

Multimodas insuper sonorum

mutationes clerici protestantur. Est enim

Mutatio apud Baccheum Alteratio

subiectorum seu Alicuius similis in

dissimilem locum transpositio. Hinc in

moralibus Mutari Gregorius inquit est ex

alio in aliud ire et in semetipsum stabilem

non esse: vnaquaeque enim res quasi tot

passibus ad aliam tendit: quot mutabilitatis

suae motibus subiacet. Verum huiusmodi

mutationem Martianus transitum appellat:

quem vocis variationem in alteram soni

figuram interpretatur. Briennius autem

mutationem dixit esse subiecti systematis ac

vocis characteris aliena ionem. Fit autem

Mutatio secundum genus quum scilicet in

tetrachordo diatonico lychanos vel etiam

paranetes chorda remittitur semitonio in

graue: transeundo in chromaticam figuram:

vel tono transeundo in enarmonicam: quae

nusquam accidit ex grauitate in acumen

variari vt Boetius noster in quarto explicuit.

Id quoque et Aristoteles ipse in musicis

problematibus intelligi voluit quum diceret

Quod sapit naturam acuti plerumque

pertransit in grauem: quod autem sapit

naturam grauis non permutatur in acutum.

Est et alia mutationis consyderatio in voce

ac sono: nam quum sunt in motu et fiunt

tantum voces et soni ipsi de genere creduntur

entium successiuorum vt vigessimo septimo

problemate interpres exposuit: [Petrus

apponensis, in margin] qua re vocis ipsius ac

soni generatio consistit in quodam fieri et

transmutari. Verum huiusmodi introductio

definitam a Marcheto consequitur

mutationem. Is enim inquit: Mutatio est

Ecclesiastics teach various mutations of

tones. According to Bacchaeus mutation is a

transposition of subjects or the like to a

different place. Thus Gregory says in

Moralia that "mutation is the movement

from one state to another which itself is not

stable, for the one tends toward the other in

the degree that it is subject to the movement

of its own mutability". But Martianus calls

such a mutation a transition, which

he explains as a "change of one tone to

another". Bryennius says mutation is "the

change of the system of a melody and of the

character of a tone". Mutation occurs in a

genus when the lichanos or par[a]nete string

of a diatonic tetrachord is lowered a semitone

into the chromatic, or a whole tone into the

enharmonic; such a change never occurs by

raising the pitch, as Boethius states in

Book 4. Aristotle also wished this to be

understood when he said in musical

Problems: "what is naturally higher tends to

descend, but what is naturally lower does not

ascend". Mutation of tone and note is also

considered in another way, for when they are

in motion and so become a melody, they are

considered a kind of moving succession, as

Petrus Apponensis has explained in the

twenty-seventh Problem. Thus the

generating of tone and note consists of a

certain motion and mutation.

But our explanation of mutation follows

the definition given by Marchettus. He

says: "mutation is the changing of the name

of a tone to another name having the same

sound".

For if certain syllables belonging to

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variatio nominis vocis in alterum in eodem

sono. Syllabae enim ipsae vocibus et

chordis suis scilicet notulis ascriptae si in

vna eademque linea vel eodem spatio

consistunt: dicuntur quantitate pares sed

qualitate seu proprietate diuersae. Inde quum

mutatio fit qualitas vnius exachordi in

alterius qualitatem transfertur stante eadem

vocis quantitate: vt testatur Anselmus tertio

suae musicae. [Anselmus. in marg.] hinc

mutationem voco alternam vocis in vocem

delationem uniformi extensione

depraehensam. Voces autem ipsas

exachordorum syllabas intelligo. Non igitur

vox mutatur in vocem per intensionem aut

remissionem sed syllaba in sillabam et

proprietas seu qualitas in qualitatem.

(Gaffurius 1496, bk. 1, ff. a viv–vijr)

their own tones and notes are situated on the

same line or space, they are called the same

in quantity but different in quality of

proprietas. Thus, mutation occurs when the

quality of one hexachord is transferred to

another having the same quantity of tone, as

Anselmus states in Book 3 of this Musica.

From this I call mutation the changing of

one tone into another tone of the same kind.

But by tones I mean the syllables of

hexachords. Therefore, a tone is not changed

into another tone by rising and falling, but

by syllable into syllable, and proprietas or

quality into another quality.

(Miller 1968, 35–36)

Following, seven treatises will be quoted, chronologically organized to provide an

overview of the concept of mutatio as it was commonly explained from the Middle Ages to

the Renaissance. Although there was no profound change of this concept through those

periods, the quotations are progressively more elaborate, in such a gradual way that reflects

the growing, humanistic concerns on the part of theorists not only to make all the

procedures and processes involved in solmization more explicit, specific, and organized, but

also to provide new and more precise interpretations of older concepts, including

propositions that might lead to specific new terminology. Concerns with elaboration are

also present in medieval writings, although they tend toward forging compromises between

statements (or glosses, or rephrasings) of earlier auctoritates (on which they are heavily

based), producing terminology that sometimes seems imprecise, and which necessitates

careful interpretation in order to solve apparent inconsistencies, and even contradictions.

113

(Each quotation will be briefly commented upon before the next one is presented. Notice

that all the quotations in this section are concerned only with the most basic concept of

mutation, which is therefore described and identified only within the realms of musica

recta—the expansion of the concept to include musica ficta will be dealt with in the next

chapter.)

Mutatio autem, secundum Guidonem

sapientissimum musice, diffinitum sic:

Mutatio est divisio unius vocis propter

aliam sub eodem signo, eadem voce et etiam

sono. Dicitur autem mutatio ab hoc verbo:

muto, mutas, quoniam unam proprietatem

vel vocem sub eodem sono in aliam

subsequentem mutamus.

(Garlandia p. 1240; CS 1: 160)

Now, according to Guido (the most wise

musician), mutation have been defined as

follows: Mutation is the division of one

syllable for the sake of another under the

same sign, the same voice, and also sound.

On the other hand, it is named after this

verb: to change (muto , mutas), because we

change one proprietas or syllable into

another subsequent under the same sound.

(my translation)

This first quotation presents a simple definition of mutation making use of the word

'vox,' which is submitted to different translations in the sentence "Mutatio est divisio unius

vocis propter aliam sub eodem signo, eadem voce et etiam sono," in order to avoid

confusion. The first occurrence must be translated as "syllable," and the second occurrence

as "voice," rendering the following version: "Mutation is the division of one syllable for the

sake of another [syllable] under the same sign [i.e., the same step-letter], the same voice, and

also sound"—the term "syllable" naturally refers to a 'solmization syllable' (a common

translation for vox), and the term "voice" may refer to a different musical phrase or melodic

gesture in another hexachordal context (whether in monophonic, or in polyphonic

situations), or may even refer to another voice in a polyphonic situation. The phrasing of

the definition given above was thereafter used as an authoritative source for paraphrases and

114

glosses by most theorists who explained mutation—Garlandia may have been the first

theorist to use this wording in the context of mutation.

Mutatio uero ut hic sumitur nihil aliud est

quam dimissio [in CS 1, divisio] uocis

unius propter [in CS 1, prope] aliam sub

eodem signo, et in eodem sono. Vnde

sequitur quod ubicumque fit mutatio:

opportet quod ibi sint due uoces ad minus.

(Lambertus ca. 1260's/1270's; I-Sc L.V.

30, f. 17r ; CS 1: 256)

In fact, as it is assumed, mutation is nothing

more than the dismissal [in CS 1, division]

of one syllable for the sake of [in CS 1, near

to] another, under the same sign (i.e., letter)

and in the same sound (i.e., step). Whence,

it follows that wherever mutation is made, it

is proper, in that place, that at least two

voices (voces, i.e., syllables) exist.

(my translation)

The second quotation (only a few twenty or thirty years after Garlandia's) is clearly

based on the first, or perhaps on some similar version that preceded both of them. There

are, however, two different wordings in the sources used in this quotation: one

(Coussemaker's edition) presents mutation as a "division (divisio) of one syllable for the

sake of another," and the other (a transcription of the manuscript L.V. 30, in the Biblioteca

Communale degli Intronati of Siena) presents mutation as a "dismissal (dimissio) of one

syllable for the sake of another." The former ("divisio") follows closely the wording of the

quotation from Garlandia's treatise, after the idea that mutation may occur when a step is

divided into two syllables. The latter ("dimissio") is used in later explanations about

mutation (especially in humanistically influenced treatises), serving as a reference to a

syllable that is being abandoned in favor of another that (applied to the same step) is being

assumed in its place. This latter wording emphasizes the description of the process of

mutation, while the former emphasizes the event; but even if the former is preserved, it must

be noted that Lambertus avoided the apparent contradiction with regard to the word "vox,"

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by elimination of its repetition in the sentence "uocis unius propter aliam sub eodem signo,

et in eodem sono" (instead of Garlandia's "unius vocis propter aliam sub eodem signo,

eadem voce et etiam sono"). Also borrowing from another paragraph used in Garlandia's

text, Lambertus goes on further to clarify that mutation can be made only where the step

contains "at least two syllables"—although Garlandia's assertion is presented in a slightly

more obscure manner.

Mutatio est variatio nominis vocis seu note

in eodem spacio, linea, et sono.

Fit namque mutatio, vel fieri potest, in

quolibet loco ubi due vel tres voces sive note

nomine sunt diverse, que quidem sub sola

una littera includuntur.

Sed quia in Γ ut, in A re, et in mi

singulariter non est nisi una sola vox sub

una littera, ideo in ipsarum aliqua mutatio

non existit.

(Marchettus 1317/18, tr. 8, ch. 2; Herlinger

1985, 280, 282; GS 3: 90)

Mutation is a change in the name of a

syllable or note lying in the same space or

on the same line and with the same pitch.

Mutation is made, or can be made, in any

location where two or three syllables or

notes are different in name but are subsumed

under a single letter.

Since on Γ ut, A re, and mi there is but a

single syllable under a single letter, there is

no mutation on any of them.

(Herlinger 1985, 281, 283)

In the third quotation (some fifty to sixty years after Lambertus), Marchettus da

Padova betrays a proto-humanistic tendency to reiterate previous definitions with

elaboration aimed at enhancing their specificity and clarity. Toward that clarification,

Marchettus mentions that a mutation can take place on a step that contains two or three

syllables in its solmization, but makes use of an extra assertion explaining that mutation

cannot happen on steps that bear only one syllable (of course, within the limits of the

recta-gamut). Significantly for the subject at hand, this strategy makes use of a rhetorical

process of 'contraposition,' which uses ideas that are contrary to each other (through simple

opposition or paradox) to prove the subject under scrutiny—this process is sometimes

116

discussed by rhetoricians under its closely related figure named 'antitheton' (also known as

'antithesis').91

Sciendum est quod mutacio, prout hic

sumitur, nichil aliud est quam unius vocis

propter aliam ad minus a se tono

differentem, dimissio in eodem loco omnino,

unde tonus est inter quamlibet vocem et

proxime sibi superiorem vel inferiorem,

preterquam inter mi et fa.

[...] sciendum est quod in manu sunt 14

loca in quibus sunt coniuncciones, seu

composiciones duarum vel plurium vocum,

et fieri possunt mutaciones [...]. Insuper

ubicumque sunt due voces ad minus tono ab

invicem distantes, ibi fieri possunt due

mutaciones, scilicet de prima in ultimam et

e converso. Et ubicumque sunt 3 voces, 6

mutaciones ibi fieri possunt, scilicet de

prima in secundam, et e converso, de prima

in terciam, et e converso, de secunda in

terciam, et e converso. [...]. Item

quandocumque, cum una mutacione habendo,

potest commode transire, non debent fieri

due vel plures, quia frustra fit per plura quod

potest fieri per pauciora.

(Anon. Berkeley 1375, tr. 1, ch. 2;

Ellsworth 1984, 48, 50)

It must be known that a mutation, as

used here, is nothing other than the exchange

of one syllable for another--which is at least

a tone away--in exactly the same place (a

tone falls between any syllable and the one

immediately above or below, except between

mi and fa.)

[...] it must be known that there are

fourteen places in the hand in which there are

conjunctions--or combinations of two or

more syllables--and mutations can be made

[...]. Moreover, wherever there are two

syllables at least a tone away from each

other two mutations can be made there: from

the first to the last and conversely. And

wherever there are three syllables, six

mutations can be made there: from the first

to the second and conversely, from the first

to the third and conversely, and from the

second to the third and conversely. [...].

Also, whenever it is possible to change over

smoothly with one mutation, two or more

ought not to be made, for what can be done

with few is wasted effort with many.

(Ellsworth 1984, 49, 51)

91 This assertion about one-syllable steps is also present in the Garlandia's treatise, although in a

position that is seemingly less efficient in its use as a rhetorical device—cf. (Garlandia p. 1240; CS 1:

160). Fairly at the same time, Lambertus also makes use of the assertion, in the same rhetorically efficient

position as Marchettus—cf. (Lambertus ca. 1260's/1270's; I-Sc L.V. 30, f. 17r ; CS 1: 256). With regard

to presentations by rhetoricians likely to have been known and used by these authors, cf. (Aristotle Rhet.,

2.19.1392a–b, 2.25.1402b, 3.9.1409b–1410b; [trans.] Roberts 1924, 129–131, 161–162, 184–186); (Anon.

ad Herennium 4.15.21, 4.45.58, s.v. 'Contentio'; [ed. and trans.] Caplan 1954, 282–283, 376–377); and

(Quintilian ca. 93/95, 9.3.81–86, s.v. 'Contrapositum'; [ed. and trans.] Russel 2001, 150–153).

117

In the fourth quotation (short of sixty years after Marchettus), one specification is

readily noted about the syllables involved in mutation: there must be at least one whole-tone

between them. This specification refers to the fact that, in the recta-gamut, no single step

includes both syllables mi and fa, and therefore, a mutation per se would not be possible,

except when its concept is expanded to include the ficta-gamut—this kind of mutation

(named ficta-mutation) will be discussed in chapter 4. The anonymous author of the

Berkeley Manuscript also summarizes that only fourteen places (in the recta-gamut—i.e.,

the hand) are available candidates for mutation, for they are the only ones that include more

than one syllable, they are: (1) C-fa-ut, (2) D-sol-re, (3) E-la-mi, (4) F-fa-ut, (5) G-sol-re-ut,

(6) a-la-mi-re, (7) c-sol-fa-ut, (8) d-la-sol-re, (9) e-la-mi, (10) f-fa-ut, (11) g-sol-re-ut,

(12) aa-la-mi-re, (13) cc-sol-fa, and (14) dd-la-sol. Furthermore, in face of several eligible

options for mutation, the treatise asserts that a mutation-step must be properly chosen, and

that the most smooth and effortless path should be adopted. The assertion, however, is

ambiguous as to whether those eligible options apply to several steps between two different

melodic gestures, or whether they apply to different pairs of syllables on the same step. In

both cases, the performer would need to choose the one step (or pair of syllables) that

would not deny the proper flow between different melodic gestures and their hexachords.

Notice that the theoretical statements from the Berkeley Manuscript can be interpreted in

two ways: (a) as reinterpretations of earlier authors (for it makes use of earlier phrasings,

expanding and also trying to integrate statements of earlier sources into a more cohesive and

concordant whole); and (b) as anticipations of an independent line of thought (for it

118

presents newly clear-cut definitions, and introduces original explanations in such a way that

ultimately tend to obscure the connection with previous auctoritates).92

Videndum quid sit mutatio. Mutatio est

dimissio unius proprietatis propter aliam,

sive variatio nominis vocis sive notae in

eodem spatio vel linea sub uno sono et

etiam sub uno signo, id est sub una littera.

Item sciendum est quod in gammaut, in

Are, in Bmi, et in Ela, nulla est mutatio,

cum in quolibet istorum non est nisi una

sola vox et opportet quod sint duae voces ad

faciendam mutationem, id est, immutando

unam vocem in aliam. Quodlibet istorum

signorum habet unam vocem et non plus, et

per unam vocem solam, mutatio non est

facienda. [...]. Item sciendum est etiam

quod in bfa bmi acuto et superacuto nulla est

mutatio. Ratio est quod omnis mutatio debet

fieri sub uno signo, ut supradictum est, et in

bfa bmi sunt duo signa, scilicet b rotundum

et b quadratum, quae habent magnam

differentiam, ut hic: . Ideo nulla est

Understanding what may be mutation.

Mutation is the dismissal of one proprietas

for the sake of another, or the variation in

the name of the syllable, or of the note in

the space or line under one sound and also

under one sign, i.e., under one step-letter

(sub una littera).

Moreover, it must be known that in

Γ-ut, A-re, B-mi, and ee-la (Ela), there is no

mutation, because in those [steps], anywhere

you care to find them, there is but only one

syllable, and it is proper that there be two

syllables in order to make mutation, i.e.,

changing one syllable into the other. Any

of those signs has one syllable and no more,

and by means of only one syllable, mutation

must not be made. [...]. And also, it must

be known that in -fa / -mi, [both] acute

and superacute, there is no mutation. The

reason is that every mutation must be made

under one sign, as it is said above, and in

-fa / -mi there are two signs, namely

92 Both interpretations may be identified as emblematic of humanistic tendencies. The

independent thought is more properly related to the Renaissance and denotes a valorization of more

contemporaneous productions. Impulses of reinterpretation, working toward the integration of earlier

auctoritates (not only through citation, repetition, or even glosses of texts taken at face-value), were more

typical of the last part of the Middle Ages (twelfth to fourteenth centuries). These impulses reflect an effort

within early Humanism (or even proto-Humanism) to forge concordances (harmonize) between apparently

discordant thoughts. This can be characteristically exemplified through the Decretum (Concordantia

discordantium canonum, ca. 1140) of Gratianus, which served to establish the later Corpus iuris canonici,

and worked to harmonize between different precepts and decrees of the Church; or through the works of

Aquinas, who sought harmonization between lay philosophical thought (Aristotelian, Neoplanotic, and

others) and theological Christian thought—cf. (Balensuela 1994, 17–47; Audi 1995, 31–34, s.v. 'Aquinas,

Saint Thomas,' 800, s.v. 'Thomism'; Hyman and Walsh 1973, 503–508; Cantor and Klein 1969, 15–17;

Weinberg 1964, 182–187).

119

mutatio, quia sicut differt b rotundum a b

quadrato, ita differt fa a mi et mi a fa. Alia

ratio est quia omnis mutatio ad minus fit per

tonum et in bfa bmi non est nisi

semitonius, scilicet fa-mi; ergo nulla est ibi

mutatio. Etiam fa et mi sunt voces mediatae

et non immediatae. [...]. Et in omnibus

aliis locis ubicumque sunt duae voces, ibi

sunt duae mutationes: exinde in Ffaut sunt

duae voces, ibi sunt duae mutationes, scilicet

fa-ut et ut-fa et sic de aliis. Item ubicumque

sunt tres voces, ibi sunt sex mutationes;

exinde in Gsolreut ubi sunt tres voces, ibi

sunt sex mutationes, videlicet: sol-re est

prima, re-sol secunda, sol-ut tertia, ut-sol

quarta, re-ut quinta et ut-re sexta. Et nota

quod non debet fieri mutatio nisi causa

necessitatis.

(Capuanus 1415; La Fage 1864, 315)

b-rotundum and b-quadratum, which have a

great difference, as here: . Therefore, there

is no mutation, because just as b-rotundum

differs from b-quadrato, so fa differs from mi ,

and mi from fa. Another reason is because

every mutation is made at least through the

whole tone, and in -fa / -mi there is but

one semitone, namely fa and mi ,

consequently no mutation is in that place.

And also, fa and mi are mediate syllables

(mediatae), and not immediate (immediatae).

[...]. And in all of the other places wherever

there are two syllables, in that place there are

two mutations: accordingly, in F-fa-ut there

are two syllables, in that place there are two

mutations, namely fa-ut and ut-fa, and thus

of the others. Moreover, wherever there are

three syllables, in that place there are six

mutations: accordingly, in G-sol-re-ut where

there are three syllables, in that place there

are six mutations, namely: sol-re is the first,

re-sol the second, sol-ut the third, ut-sol the

fourth, re-ut the fifth, and ut-re the sixth.

And take notice that mutation must not be

made except for the sake of necessity.

(my translation)

(underlines mine)

In this fifth quotation (forty years after those of the Berkeley anonymous), Nicolaus

Capuanus can also be interpreted in the same two ways as the previous quotation:

reinterpretations of earlier sources, plus elaboration of independent opinions. Among the

steps that are singled out as ineligible places for mutation, noteworthy is the inclusion of

ee-la, which was not often mentioned explicitly in historical treatises of previous centuries.

Another point is the presence of explanations about -fa / -mi, which cannot be taken as a

place for mutation, due to its dual nature (i.e., due to being conceived as a double-step).

120

Additionally, near the end of the quotation, Nicolaus introduces a qualification of a

subliminal rhetorical nature, applied to the solmization syllables fa and mi (representing the

internal semitone of a hexachord): they are qualified as mediatae et non immediatae (i.e.,

"mediate syllables, and not immediate"). Immediate things (or meanings) are those that are

close together, or are so close that they can even be found in the same place (i.e., they can be

congruent, and they can exist as two versions of the exact same thing). In solmization

terms, this is the case with mutation itself, for in a step (one place) that bears two syllables

(two meanings), mutation can be made, and so the two syllables can be qualified as

"immediate." Mediate things (or meanings), however, are not classifiable as commonalities,

they share no intersection, they are separate by default, although one thing may imply the

existence of the other. In solmization terms, it applies perfectly to the double-step

-fa / -mi, since both fa and mi are represented in the same graphical place (whether in the

Guidonian hand or on a staff), but have two different meanings, and so can only be qualified

as "mediate." This kind of explanation is intersects with the figures of rhetoric called

'disiunctio' and 'coniunctio'—two opposing types of sentences related to 'zeugma.'93

93 'Zeugma,' according to Lanham, is "[a] kind of Ellipsis in which one word, usually a verb,

governs several congruent words or clauses"—cf. (Lanham 1996, s.v. 'Zeugma'); cf. also (G. Burton

1999-2004, s.v.'Zeugma'). In other words, a 'zeugma' happens in a sentence with two or more clauses, all

of them sharing a common word (e.g., a verb, or noun, or verbal noun, etc.) that is, however, present in

only one of the clauses and omitted in the other(s). For example: "Fades physical beauty with disease and

age" ("Deflorescit formae dignitas aut morbo aut vetustate")—cf. (Anon. ad Herennium, 4.27.38; [ed. and

trans.] Caplan 1954, 322, 323). There are usually three different types of 'zeugma' identified in rhetoric,

defined according to the position of the common word within the sentence: 'prozeugma,' when the word is

placed at the beginning of the sentence (as in the above example); 'hypozeugma,' when it is placed at the

end (as in "Either with disease or age physical beauty fades"—"Aut morbo aut vetustate formae dignitas

deflorescit"); and 'mezozeugma' (also called 'synzeugma'), when it is place in the middle of the sentence (as

121

Coniunctio happens when a word (common to all clauses in a sentence) is place in the

middle—it is, in fact, referred to as a synonym for 'mezozeugma.' Disjunctio is also a

sentence containing two or more clauses related to one and the same matter as with the

zeugma, but each clause has its own individual verbs—this figure is sometimes considered

the opposite of a zeugma, and is therefore used as a synonym for 'hypozeuxis.'94 The terms

used by Capuanus are also related to different types of inference (interpretation, deduction)

drawn from a 'syllogism,' according to the number of premises used: 'mediate inference' is

one that draws conclusions from a syllogism that has two premises (in musical terms,

equivalent to the double-step -fa / -mi); 'immediate inference' is one that draws

conclusions from a syllogism that has only one premise (in musical terms equivalent to a

single step-letter that may, however, contain two or more different syllables)—cf. (Lanham

1996, s.v. 'mediate inference'). Now, with regard to naming mutations, the anonymous

Berkeley Manuscript (quoted earlier) described which pairs of syllables may be involved in

mutation in a different way; there the author said only that in a two-syllable step the

mutations would be two (first to third, and third to first), and that in a three-syllable step the

mutations would be six (first to second, second to first, first to third, third to first, second to

in "Either with disease physical beauty fades, or with age"—"Formae dignitas aut morbo deflorescit aut

vetustate")—idem.

94 One example of disiunctio is: "By the Roman people Numantia was destroyed, Carthage razed,

Corinth demolished, Fregellae overthrown" ("Populus Romanus Numantiam delevit, Kartaginem sustulit,

Corinthum disiecit, Fregellas evertit"—cf. (Anon. ad Herennium 4.27.37; [ed. and trans.] Caplan 1954,

322, 323). Disiunctio and hypozeuxis may be considered cases of 'synonymia,' if they are understood as a

series of related statements, each one employing different words, but whose meaning is approximately the

same. If one considers that disiunctio is an omission of grammatical conjunctions that could be used to

link the clauses, then it ought to be made synonymous to 'asyndeton' (sometimes spelled 'asyntheton').

122

third, and third to second), but he mentioned no syllables or steps by name. Previous

treatises (and many others during the Renaissance) would present each step by means of

their full designation, followed by indications of each individual mutation. Nicolaus

Capuanus, however, does the same in a more brief, hybrid way, by naming only two steps: a

two-syllable step (F-fa-ut), and a three-syllable step (G-sol-re-ut), followed by indications

of individual mutations restricted to only those two steps—implicitly, they would then serve

as models for all the others. Finally, the last statements in the quotations from Capuanus

and the anonymous Berkeley author can be interpreted by emphasizing their similarity: one

says that mutation must not be made where it is not necessary, and the other says that

mutation must be smoothly made. In either case, it means that mutation must be avoided if

there are other alternatives, but if implemented it must be done as scrupulously and

seamlessly as possible.

[M]utatio est unius vocis in aliam variatio.

Omnes autem voces sunt mutabiles, sed

aliae plus aliae minus.[...].

In Γ ut autem, in A re, in mi, et in e

la, mutatio nulla fit, eo quod in quolibet

ipsorum locorum sola vox est. Ubi vero

sola vox est mutatio fieri non potest,

quoniam in omni mutatione fienda duae

voces requiruntur, scilicet una quae mutatur,

et alia quae per ipsam mutationem

assumitur. Praeterea in fa mi acuto et

superacuto, nulla fit mutatio, quia mutatio

habet fieri necessario per duas voces unisono

convenientes, id est quod vox illa quae

mutatur et alia quae per mutationem ipsam

assumitur sint in uno et eodem sono, sicut

fa et ut de C fa ut, sol et re de D sol re, et

Mutation is the variation of one syllable

into another. All syllables, however, are

mutable (mutabiles), but sometimes more

sometimes less. [...].

However, no mutation is made in Γ-ut,

in A-re, in B-mi , and in ee-la, [and] that

because in any one of the places themselves

the syllable is alone. To be sure, where the

syllable is alone a mutation cannot be made,

since two syllables are required in every

mutation about to be made (fienda), namely

one that is mutated, and another that is

assumed [i.e., adopted] through the mutation

itself. Moreover, in -fa / -mi [both] acute

and superacute, no mutation is made,

because a mutation has to be made

necessarily through two syllables converging

123

sic de aliis. Unde quom fa et mi in quovis

loco numquam sint in uno et eodem sono,

immo ab invicem distent maiori semitonio,

est impossibile quod unum in alterum sit

mutabile.

Nec praetereundem est quod mutationes

inventae sunt propter digressum unius

proprietatis ad aliam. Unde postquam

aliquam proprietatem ingressi sumus, ante

finalem eius vocem mutare nunquam

debemus, et sic intelligitur quod rarius ac

tardius ut fieri potest mutandum est; denique

mutatio cuiuslibet vocis non est soni sed

nominis ipsius. Unde quando solfisamus,

tantum mutamus quia tunc voces nominatim

exprimimus, namque solfisatio est canendo

vocum per sua nomina expressio.

(Tinctoris p. 1477, ch. 7; Seay 1975–78, 2:

48, 52; CS 4: 10, 12-13)

in a unison, that is, because that syllable,

which is mutated, and the other, which is

assumed through the mutation itself, are in

one and the same sound, like fa and ut from

C-fa-ut, sol and re from D-sol-re, and so

from others. Whence, [steps] with fa and mi

are never [found] in one and the same sound

in any place. More precisely, [since] they

are mutually distant by a major semitone, it

is impossible that one be mutable into the

other.

It must not be overlooked that

mutations have been invented because of a

digression of one proprietas into another.

Whence, after we have entered in some

proprietas, we should never mutate before its

final syllable, and thus, be it known [that],

insofar as it must be mutated, it can be made

more rarely than tardy. Of course, mutation

of any voice is not [mutation] of sound, but

[mutation] of the name (i.e., syllable) itself.

Whence, when we solmize, we only mutate

because in this way we express the syllables

by name, for in fact solmization (solfisatio)

is to sing a syllable through its own distinct

name.

(my translation)

In the sixth quotation (about sixty years later than the one drawn from Capuanus's

treatise), some sentences invite clarification. For instance, in the sentence "All syllables,

however, are mutable, but sometimes more sometimes less" ("Omnes autem voces sunt

mutabiles, sed aliae plus aliae minus"), the qualification mutabiles (as a possibility) allows

for the understanding that 'any solmization syllable is prone to mutation.' Of course, the

actual occurrence of a mutation will depend on the need for a hexachordal change, and on

the possibility of pairing one syllable with another on the same step. In this light, the

supplementary assertion "sometimes more sometimes less" might be interpreted as a

124

reference to "more" when there are more syllables in the same recta-step, and "less" when

there are less syllables; i.e., in C-fa-ut there are less possibilities (only two: from fa to ut,

and from ut to fa), but in c-sol-fa-ut there are more possibilities (up to six: from sol to fa,

and vice versa, from fa to ut, and vice versa, from ut to sol, and vice versa). In the third

paragraph, the assertion that "mutations have been invented because of a digression of one

proprietas into another" ("mutationes inventae sunt propter digressum unius proprietatis

ad aliam") is Tinctoris's way of rephrasing statements already provided by earlier

theorists—e.g., Garlandia and Capuanus, quoted above, and Cochlaeus, quoted below. As

mentioned in chapter 2, proprietas is taken as synonymous of hexachordal family: durum

proprietas (all hexachords that contain the -durum or its octaves), natura proprietas (all

hexachords that contain no variety of b), and molle proprietas (all hexachords that contain

the -molle variety, or its octaves). In this capacity, a mutation from a -hexachord to a

-hexachord would not denote a change (or digression) with regard to proprietas, since

they both pertain to the durum-family (although one is a recta-hexachord, and the other is a

ficta-hexachord). In all cases, however, one must remember that references to proprietas (in

the above quotations) apply only to mutation within the recta-gamut, for these treatises are

presenting only basic concepts about mutation. Thus, any mutation within a recta-only

environment would necessarily represent a change in proprietas, since the only three types

of recta-hexachords ( , , and ) are also individual representatives of the three

proprietates. If the clause was to include the ficta-gamut, it would need to provide a more

generic statement, by saying that 'mutations had been invented because of a digression (a

125

change) from one hexachord into another,' thus allowing for changes between hexachords

within the same family, as made clear the excerpt from Gaffurius's treatise (1496, bk. 1, ff. a

vijr; Miller 1968, 36) quoted above. Notice, however, that in most treatises mutation per se

is first presented in its specific, restrictive sense as a procedure that applies to a recta-only

context, and when a ficta context (or even a merged context) is meant, then another species

of mutation is presented. Different species and subspecies of mutation (as well as the

distinct types and cases that shape their differences) shall be discussed in the next chapter.

Tinctoris's quotation also elaborates on other explanations, such as on the idea that mutation

must not be used unless absolutely necessary (as also stated before the Anon. Berkeley and

Capuanus). Emphasizing this precept, Tinctoris goes further by asserting that if a mutation

is inevitable, then the scrupulously chosen places of mutation must be as few as possible

("more rarely"—"rarius"), or else be delayed as much as possible ("more

tardy"—"tardius").

Quid est mutatio? Est vnius vocis in

aliam in eadem claue vnisona

variatio. Vocem dico, non sonum, sed

syllabam, quoniam idem est vtriusque vocis

in eadem claue sonus, at non eadem syllaba:

nec eadem proprietas. Mutatur itaque syllaba

in syllabam et proprietas in proprietatem.

In bfa mi cum ambae voces non sint

vnisonae, non potest ibi proprie

fieri mutatio. [...].

Fit autem Mutatio triplici de causa.

Primo ad concipiendum suauioris

modutalionis transitum: Ad quem saepe non

minus facit, variata vocum qualitas, quam

What is mutation? It is the change of

one vocable (vox) into another on the same

pitch. I call vox not a sound but a syllable,

because the sound of each tone on the same

key is the same, but the syllable and

property are not the same. So one syllable

changes into another and one property into

another.

The two vocables b fa 5 mi are not a

unison, and a mutation cannot occur on

them properly. [...].

A mutation is made for three reasons:

1. In order to make a more pleasant melodic

transition, in which the quality of a tone is

changed no less frequently than the size of

126

permutata soni modulati quantitas. Secundo

vt infra et supra vnumquodque Hexachordum

voces liceat intendi et remitti. Tertio ad

faciliorem Diatesseron ac Diapente transitum

in tonorum permixtione, Nam quilibet tonus

octauam regulariter continet.

(Cochlaeus 1511–14, tr. 2, ch. 8, f. B vv)

the tone.

2. To permit tones to go above and below a

hexachord.

3. To facilitate the exchange of a fourth and

a fifth in a mixture of Tones, for each Tone

normally comprises an octave.

(Miller 1970, 42)

The seventh quotation (thirty to forty years after Tinctoris) denotes a stage of

elaboration that attempts to summarize the essential aspects of mutation, at least according to

Cochlaeus's understanding. In the first paragraph, in addition to rephrasing definitions

based on earlier auctoritates, Cochlaeus strove to clear whatever ambiguity of meaning may

have remained in relation to the term 'vox.' He then proceeded to enumerate of those aspects

(considered decisive to understanding and implementing mutation). In the words "more

pleasant melodic transition" ("suauioris modulationis transitum"), Cochlaeus is suggesting

the same idea of seamless change implied by the anonymous Berkeley author in the clause

"to change over smoothly with one mutation" ("cum una mutacione [...] commode

transire"). Both clauses invite sensations and attitudes that may lead performers to obtain

pleasantness or smoothness of solmization—whether that can be accomplished by avoiding

mutations, implementing what has been prescribed, or even by forging an artificial situation,

will depend on necessity, taste, or even ability.95 He also mentions that mutation is done to

implement a change of quality ("qualitas") on one specified sound ("sonus")—by which he

95 The rhetorical appeals embedded in the original texts (in these as well as in most historical

treatises) are certainly meant to impress subjectively whoever undertakes their study, in order to enhance the

understanding with more compelling means than just objective definitions can provide.

127

means a change in the "proprietas."96 Still with regard to the first item of Cochlaeus's

enumeration, the words "quam permutata soni modulati quantitas" must be rendered with a

different translation, generating the following sentence: "First, in order to make a more

pleasant melodic transition, in which the quality (qualitas) of a tone is changed no less

frequently than the quantity (quantitas) of the melodic sound"—by quantitas, Cochlaeus is

referring to the number of syllables that each step utilizes in its full designation. In this

light, the first statement means that 'in order to produce a seamless, natural, unambiguous

mutation, one must observe the number of syllables in each step, so neither are the

mutations done in a greater number (or more often) than necessary, nor are the proprietates

(or the hexachords) changed more often (or in a greater number) than the step can admit.'

In the second item of his enumeration, Cochlaeus provides a more direct assertion that

'mutation is done in order to allow a solmization beyond the limits of only one hexachord,'

for it is implied that melodies generally reach beyond the intervallic configuration and

compass (tonus-cum-diapente) of the Guidonian hexachord. The third item also capitalizes

96 In Cochlaeus's treatise, the terms qualitas and proprietas are used interchangeably. However,

the term "proprietas" seems to entitle a different translation than Miller's choice of "property." A translation

into "propriety" would seem more appropriate, when observing the differentiation between "proprietas" and

"proprium" given by Gaffurius in his Practica musice, a work which Miller has translated two years before

Cochlaeus's treatise—cf. (Miller 1968, 33–34). Gaffurius (1496, bk. 1, ch. 4, f. a vir) specifically

discusses the proper use of those terms, by saying that "proprietas" has an "abstract" sense ("abstractum"),

and "proprium" a "concrete" sense ("concretum"). In his translation of Gaffurius's treatise, Miller chose to

maintain the Latin form of those terms, instead of providing English renditions as he did with Cochlaeus's

treatise. Nevertheless, Miller mentions that the source for Cochlaeus's treatise (at least for ch. 8 quoted

above) was "almost certainly Gaffurius" (Miller 1970, 42n). (In another translation of Gaffurius's Practica

musicae released roughly one year after Miller's, Irwin Young suggests that the term "proprium" should be

translated into "property," and "proprietas" into "propriety.") Throughout this dissertation, the untranslated

word 'proprietas' has been preferred, having 'propriety' as its most appropriate translation when needed.

128

on the previous assertion, by emphasizing that melodies usually go beyond the hexachordal

limits, since solmization often faces transitions between a diapente and a diatessaron (which

characterize the modal contents of the music). The objective here, in fact, is to state that the

performer (or even the theorist, or composer, or copyist) has to be able to aurally understand

how to apply hexachordal solmization to the recognition of the appropriate mode that

shapes the melody. These quotations shall then suffice as background information to more

practical explanations about mutation.

As mentioned above (in the last section of chapter 2), mutation can be conceived as a

procedure very similar to the modern concept of harmonic modulation from one key to

another, in which one or more chords are chosen as mediators.97 In that type of

modulation, the chosen chord (or chords) needs to be common to both keys, and therefore

provides a link between them. The tonal function and label applied to the chosen chord,

however, will vary with respect to which key is being considered (whether the previous or

the subsequent key) at a given instant. Similarly, in order to make a mutation, one step must

be chosen as mediator between the two hexachords involved in the solmization of that

gesture and will need to pertain to both the previous and the subsequent hexachord,

although its function and label (i.e., its individual step-designation by means of the

solmization syllable) will vary with respect to each particular hexachord; i.e., the

97 Modern musicians who have learned some kind of 'moveable-do' solfege will also relate the

process of mutation to a similar process of melodic modulation—e.g., when one must move the syllable

'do' to a pitch different than the one to which it was first applied, notedly due to a tonal modulation—cf.

(NHarvard 1986, s.vv. 'Fasola,' 'Solfège, solfeggio,' and 'Tonic Sol-fa'; NG 2e, s.vv. 'Fasola,' 'Solfeggio,'

'Tonic Sol-fa').

129

step-designation will vary in each hexachordal context by means of different solmization

syllables. In many cases more than one step is eligible as a representative of mutation, but

eventually only one step will be singled out to fulfill that role. For instance, if a step such as

c-sol-fa-ut is chosen as an appropriate place of mutation, with a transition needed from the

-hexachord to the -hexachord, then that step will bear the individual designation c-fa in

the -hexachordal context, and c-ut in the -hexachordal context. Similarly, a mutation can

be made from sol to ut if the melodic gestures imply that a transition has to be made, on

that same step, between the - and the -hexachords.

Historical treatises presented mutations by explicitly describing every single

mutation within a single recta-step, usually in one of three different ways: (a) sometimes the

presentation spelled out the mutations for every single step throughout the entire gamut; (b)

sometimes for only a few steps within a chosen octave, or some other intervallic span

(implying that the others would follow the same procedure); or (c) simply for one or two

steps with different designations (e.g., as exemplified in the quotation above from Capuanus

for the steps from F-fa-ut to G-sol-re-ut).98 Through such presentations, authors

emphasized not only the number (quantitas) of mutations that can be made (or admitted)

within each step, but also that a mutation can occur in either direction; i.e., steps with two

98 In the treatise Expositio manus (p. 1477), in the large part omitted in the quotation given

above, Tinctoris produces yet another way of spelling out mutations. Although he additionally presents

them by means of the (a)-type of presentation, Tinctoris presents all the possible mutations for each

syllable, given the restrictions of the full designations of the recta-steps, mentioning a total of eighteen

mutations: ut-fa, ut-sol, ut-re, re-sol, re-la, re-mi, mi-la, fa-sol, sol-la, which adds up to nine, and their

converse, which adds another nine.

130

syllables in their designation admit two mutations (one ascending and the other descending),

and steps with three syllables admit six mutations (three ascending, and three descending).

The nomenclature of 'ascending' versus 'descending' is applied to the interval following the

second syllable in a mutation (i.e., the syllable that is being reached or assumed), which

often denotes also the direction in which the new melodic gesture will follow in relation to

the previous melodic gesture. When the three lower syllables of the hexachord (ut, re, mi)

are reached, the melodic motion should ascend, since there is little room for a descent;

conversely, when the three upper syllables (fa, sol, la) are reached, the melodic motion

should descend, for if the melody proceeded upwardly, then the limits of the hexachord

could soon be reached or exceeded, and thus motivate the need for another mutation.99

Therefore, these determinations about ascending or descending intervals (and the expected

motions of the melodic gesture that occurs subsequently to the place of mutation) are

essential to the concept of mutation (and to hexachordal recognition), illustrating the limits

that theorists were trying to explain.

Nota quod omnis mutatio in ut, vel in re,

vel in mi, desinens, talis dicitur ascendens.

Similiter omnis mutatio in fa, vel in sol,

vel in la desinens, talis dicitur descendens.

(Garlandia p. 1240; CS 1: 160)

Notice that every mutation [with] endings in

ut, or in re, or in mi are said, as such,

[when in] ascending [motion]. Similarly,

every mutation [with] endings in fa, or in

sol, or in la endings are said, as such, [when

in] descending [motion].

(my translation)

————————

99 Additional explanations on those three-syllable subsets will be given in chapter 4 .

131

Desinentes in ut vel in re vel mi semper

ascendere dinoscuntur; sed omnes aliae

mutationes in fa vel in sol vel in la

desinentes, ubicumque fuerint, deprimuntur.

(Petrus dictus Palma ociosa 1336; SIMG

15: 515–516)

[Mutations with] endings in ut or in re or

in mi are always discerned in ascending

[motion]; but all other mutations with

endings in fa or in sol or in la are made in

descending [motion] (deprimuntur, i.e., are

pressed downward), wherever they may

occur.

(my translation)

————————

Et nota quod non debet fieri mutatio nisi

causa necessitatis. Item sciendum est quod

omnis mutatio quae fit in ut aut in re, aut in

mi dicitur ascendendo, quia plus habet

ascendere quam descendere; et omnis mutatio

quae fit in fa aut in sol, aut in la dicitur

descendendo, quia plus habet descendere quam

ascendere.

(Capuanus 1415; La Fage 1864, 315)

And notice that you must not make a

mutation unless because of necessity.

Likewise, it must be known that every

mutation that is done in ut, or in re, or in

mi , is said [when] in ascending [motion],

because it has more to ascend than to

descend; and every mutation that is done in

fa, or in sol, or in la, is said [when] in

descending [motion], because it has more to

descend than to ascend.

(my translation)

These explanations about ascending and descending motions (of which Garlandia's

seems to be the earliest) also recall Gaffurius's quotation of Aristotle on that subject given

above (p. 112). Aristotle's original assessment reads:

Why is it more satisfactory to pass from a high to a low note than from a low to a high note? Is

it because the former amounts to beginning at the beginning, for the mese, or leader, is the highest

note in the tetrachord? But in passing from a low to a high note one begins not at the beginning

but at the end. Or is it because a low note is nobler and more euphonious after a high note?

(Aristotle Problem. 19.33; [trans.] Forster 1984, 1434–1435)

The assessments (in all the above quotations) also function as rhetorical and

philosophical explanations of sensations and attitudes the performer was expected to

perceive and achieve, in order to facilitate the practice of mutation in particular and of

solmization as a whole. The next section will provide appropriate melodic illustrations for

132

mutation and its processes of execution, while suggesting some guidelines that might enable

the smoother way to 'mutate.'

(ii) Mutation (basic cases, processes and guidelines)

One of the first problems faced by performers during solmization is 'where to

mutate,' i.e., determining the exact place of mutation. In the most basic process (or case), as

asserted in the quotations above, a performer would be required to think of one syllable

(from the hexachord being solmized) and immediately utter another (based on the

subsequent hexachord). There were of course other ways for executing a mutation, as shall

be explained below, but the 'mental' process described in the following quotations was

regarded as the most effective and appropriate.

De Mentalj vocum mutatione.

Caput IX.

Quid est mutatio Mentalis? Est quando vna

vocum canitur et altera mente tenetur. Aptior

est haec mutatio quam prior, Exprimere

nanque ambas syllabas est notam geminare:

quod nec auribus gratum est, nec cantui

conueniens: Immo vero in cantu mensurali

omnino intolerabile in minutis presertim

figuris, vbi velocitas notarum geminationem

non admitteret. Quare a mutatione explicita

solummodo est incipiendum. In implicita

vero perseuerandum, eique asuescendum.

(Cochlaeus 1511–14, tr. 2, ch. 9, f. B vir)

CHAPTER 9

Mental Mutation of Vocables

What is a mental mutation? It means to

sing one vocable and to keep the other in

mind. This kind of mutation is more

suitable than the prior kind, for singing both

syllables means singing the same note

twice, which is neither pleasing to the ears

nor fitting in a song. Moreover, in

mensural music it is completely intolerable,

especially in smaller note values in which

the speed of the notes does not allow a

repetition of the same note. Thus explicit

mutation is considered only as a beginning,

but implicit mutation is its continuation and

practical application.

(Miller 1970, 43)

133

————————

CAPVT TERTIVM

DE MVTATIONE VOCVM

quae ad Solmizationem perquam

necessaria est

Mvtatio musica, est vnius vocis in

aliam, in eadem claue, vnissona variatio, ob

vocum paucitatem et cantus pluralitatem

reperta, Ad quam duae necessariae sunt

voces. Vna dicitur mutata, quae per

mutationem relinquitur, Altera mutans, quae

loco vocis mutatae assumitur.

Est igitur duplex mutatio, Explicita, in

qua vox mutans et mutata ambae

exprimuntur, haec alio nomine vocalis

dicitur, Implicita siue mentalis est, in qua

vna vocum canitur et altera mente tenetur.

Aptior est haec quam illa, Exprimere namque

ambas syllabas, est notam geminare, quod

nec auribus gratum est, nec cantui

conueniens, imo vero in cantu mensurali

omnino intolerabilis, in minutissimis

presertim figuris, vbi notularum velocitas,

geminationem non admittit.

(Rhau 1517, ch. 3, f. C iir–v)

CHAPTER THREE

ON THE MUTATION OF SYLLABLE

which is extremely necessary

to Solmization

Musical mutation is [when] one syllable

[is made] into another, in the same

step-letter, [it is] a variation on the unison,

due to a paucity of syllables and to

conspicuous surplus of melody. With

respect to that, two syllables are necessary:

one is called "mutated" (mutata), which is

omitted in the mutation, and the other [is

called] "mutant" (mutans), which is adopted

in lieu of the mutated syllable.

Therefore, mutation is twofold: Explicit

(or Simple), in which both the mutant and

the mutated syllable[s] are articulated,

[where] one vowel is said through another

name; Implicit (or Intricate) or mental is

[that] in which one syllable is sung and the

other is kept in the mind. The latter is more

efficient than the former, for in fact to

articulate both syllables, is to double the

notes, because it is neither pleasing to the

ears, nor convenient to singing. Indeed, in

measured music (cantus mensuralis) [it is]

completely intolerable, especially on the

smallest note-shapes (figurae), where the

speed of the notes do not allow doubling.

(my translation)

Given the context described by both Cochlaeus and Rhau, the "explicit" case of

mutation was not the most usual procedure, and the "implicit" case of mutation was the

preferred and most common. Although these two quotations were drawn from

humanistic-inspired sixteenth-century treatises, there is no reason to assume that mutations

134

were executed by any other means. At least as early as the mid-thirteenth century, similar

assertions can be found in which the 'explicit' is hardly mentioned, and the definitions of

mutation per se are based rather on the 'implicit' case—e.g., as in the assertion, quoted above

in p. 115, that "mutation [...] is nothing more than the dismissal of one syllable for the sake

of another" ("[m]utatio [...] nihil aliud est quam dimissio uocis unius propter aliam"),

provided by Lambertus (ca. 1260's/1270's; I-Sc L.V. 30, f. 17r; my translation). As both

Cochlaeus and Rhau explain, the primary reason for favoring a "mental" or "implicit"

mutation (instead of "explicit" mutation) is rather obvious: one cannot sing two syllables at

the same time on the same note, unless the note is fractioned (divided) into two (which

would be even more confusing when the rhythm is already prescribed—as in "measured

music"). Nevertheless, there is no doubt that 'explicit' mutation is the easiest process, and

the simplest manner of execution, since both syllables are uttered, one after the other. This

character of ease and simplicity seems corroborated in Cochlaeus's assertion, given above,

that "explicit mutation is considered only as a beginning" ("mutatione explicita solummodo

est incipiendum"), which leads to the interpretation that 'explicit mutation' may have been

common practice among students in their earliest stage of learning.100 In light of this, the

viability of 'explicit' mutation is the first procedure one must consider in solmization, and

since one needs to utter consecutively two syllables on the same step, one of the best places

must be at note-repetition instances. Thus, the first guideline concerns the appropriate

choice for a mutation-step that will enable execution of the easiest and simplest case of

100 This is a stage of learning previous to that first stage of reading discussed in chapter 2 (ii).

135

mutation ('explicit'): in order to mutate, the reader is advised to look for places where there

is a repetition of one single step consecutively, or else where there is a unison

note-repetition. Such a guideline might even provide some insight regarding the

interpretation (performance inflections) of note-repetitions in plainchant-melismas.

Certainly neither all repeated (or repercussive) notes in a chant are definite signs for

mutation, nor an 'explicit' mutation may explain all instances of note-repetition (whether in

monophonic or in polyphonic performance). However, when a note is repeated and can be

chosen as a step for mutation, then the first note will naturally be solmized according to the

previous hexachord, and the second note according to the hexachord that follows. The next

quotation, from Ornithoparchus's Musice active micrologus (1517) corroborates the idea

that note-repetition is appropriate for 'explicit mutation' (which he calls "vocall").

Mentalis, non vocalis mutatio facienda est,

nisi due vt tres note ponantur in eodem loco

mutabili.

(Ornithoparchus 1517, bk. 1, ch. 6, f. C [ir])

You must make a mentall, not a vocall

Mutation, unlesse two or three Notes be put

in the same place that receiues Mutation.

(Dowland 1609, 17)

Statements given in this and previous sections also indicate that a mutation is a

change of syllables that depends on the unison. Since the performer has to be able to

maintain the unison, repeated (stressed) notes are a good place for executing a mutation.

The reason for this is that a mutation can only happen when the performer has a clear

perception of the sound of the chosen step—thus, mutation is also dependent on the

memory of the sound itself. Consequently, the best place for mutation is on a step that can

be well-ingrained (aurally) in the mind of the performer (whether or not it occurs as

consecutively repeated notes). In other words, a step that frequently recurs in the course of

136

the piece (monophonic or not) has better chances of serving as a mutation-step (for it is

aurally remembered with more ease) than another step that appears only a few times in the

whole work. Thus, a second guideline (concerning aural perception) may be inferred: in

order to mutate, the reader should preferably choose among those steps that predominate

(aurally) throughout the entire piece. In relation to modes (ecclesiastical or not), steps that

are notable candidates for mutation might be found not only among those that tend to be

repeated, or that tend to polarize the melody (e.g., the 'dominans' of a mode), but also those

that serve as the ultimate referential steps for determining the mode itself (e.g., the 'finalis'

and 'cofinalis'); this may be extended to include steps that serve to emphasize any of the

primary ones.101 Although no reference was found in the course of this research (either in

medieval or Renaissance treatises) that explicitly assigned mutations to dominantes, finales,

cofinales, or the like, the aural prominence of these notes is frequently a sufficient reason to

use them as possible mutation-steps. In another approach, it may be said that if two

101 The Latin term 'dominans' (or its modern equivalent 'dominant'), when applied to modes,

indicates those steps which are most likely to be repeated in a psalm-tone formulae, or, as mentioned above,

to dominate or polarize a melody around itself. Medieval authors usually referred to these polarizing modal

steps by terms such as 'tubae,' 'tenores,' and others (but scarcely 'dominans' itself). Modernly, the English

equivalent 'dominant' has been adopted by some influential scholars—cf. (Apel 1958, 135–137 ff.; Hoppin

1978, 64–67); although a greater number of other scholars seem to have preferred the Latin 'tenor'—cf.

(NHarvard 1986, 499–501, s.v. 'Mode'; Atlas 1998, 94–97; Harold S. Powers, in NG 2e, s.v. 'Mode,' esp.

§ II–III). Even though ' tenor' seems to be a more convenient term, it also seems more confusing, since that

same spelling has two other meanings: as a voice-register (tenor); and as 'recitation tone.' The English

spelling of the former term ('dominant') also presents confusions, mostly because of its application as a

chord function (or as a functional region) in modern harmonic analyses. In this dissertation, the Latin

spelling 'dominans' has been adopted since it emphasizes the meaning as a pivotal step; one that polarizes

the melody around itself. Besides the 'dominans,' however, a modal melody may occasionally rely on other

recurrent, circumscribing steps, which can just as well be considered for mutation.

137

interlocking hexachordal gestures involve any of them, and if they are considered among the

possible places for mutation, then the choice will more likely fall there than on any other

step. Connections between modes and hexachords—found in some treatises from the

late-thirteenth and early-fourteenth centuries—are usually restricted to the use of

solmization syllables as means for the description of modal structures, or as means for the

denomination of referential steps within a mode. The latter situation occurs, for example, in

relation to the finales, for which specific solmization syllables are assigned: re to the

protus, mi to the deuterus, fa to the tritus, and sol to the tetrardus.102 There were, of

course, historical treatises that described modal structures by means of solmization

syllables—most emphasizing the intervallic formation or representative octave-scale of each

mode. There were also other treatises showing assertions that solmization depends on the

prior identification of the mode upon which the melody is composed. In all cases no

mutation or specific procedures to solmize modes is given (only solmizations syllables

serving as means of description). For instance, in the chapter "De solfizatione regule" (lit.,

"On the rules for solmization," or "Of Solfaing" according to John Dowland's translation)

102 The earliest explicit references, in this fashion, connecting hexachordal syllables to the 'finals'

('finales'), and to the 'cofinals' or the like ('affinales' or 'confinales,' and also 'consociales' or 'sociales'), are

those found in Hieronymus de Moravia's Tractatus de musica (p. 1272, ch. 21; CS 1: 77–78), and Jacobus

Leodiensis's Speculum musicae (p. 1330, bk. 6, ch. 75; CS 2: 313; Bragard 1973, 6: 217). See also

Harold Powers's entry in The New Grove Dictionary (NG 1, 12: 391–396, esp. § II.4; NG 2e, s.v. 'Mode'),

and Dolores Pesce's The Affinities and Medieval Transposition (1987)—the latter is an invaluable work (in

both assessments, references, and documentation) on modal concepts and their correlations with hexachords,

solmization, and ficta.

138

of his treatise, Andreas Ornithoparchus presents a set of twelve rules, of which the first and

the fifth are quoted below.

Prima. Solfizans cantum aliquem, pre

omnibus tonum respiciat, necesse est. Toni

enim cognitio, est schale: sub qua cantus

decurrit, inventio.

[...]

Quinta. Omni solfizanti videre erit

necessarium, an cantus regularis existat, nec

ne. Cantus enim transpositio, mutationis

schale plerumque est occasio.

(Ornithoparchus 1517, bk. 1, ch. 5,

f. B iijv–[ivr])

The First, He that will Solfa any Song,

must aboue all things haue an eye to the

Tone. For the knowledge of the Tone is the

inuention of the Scale, vnder which it

runnes.

[...]

The Fift, Euery Solfaer must needs looke,

whether the Song be regular, or no; for the

transposition of a Song is oft times an

occasion of changing the Scale.

(Dowland 1609, 15)

(underline mine, italics in original)

As in other previous quotations, the assertions from this mid-Renaissance treatise

were also derived from the same precepts followed by medieval theorists, and were still

being used by later generations.103 Notice, however, that the identification of certain modes

103 Ornithoparchus's set of "rules for solmization" also provided the basis for Lanfranco's, who

elaborates on them, and addresses the singer more directly than Ornithoparchus. Lanfranco also divides the

rules in two groups appearing in two different sections of his Scintille di musica (1533): one group of rules

is entitled "General rules for solmization" ("Regole generali per la solfizatione"; pt. 1, f. B [ir]); and the

other "Of some rules for the singer" ("Di a'cune regole per lo Cantante"; pt. 3, ff. G [viiiv]–H [ir]). Still

another similar set of rules is given in Johannes Spangenberg's Quaestiones musicae (Nuremberg, 1536).

Prima. Solmisans in primis tonum cantus respiciat necesse est. Qui enim cantum sine toni

agnitione canit, idem facit quod is, qui Syllogismum extra modum & figuram componit.

(Spangenberg 1536, f. B7r)

First rule: He who solmizes must first consider the mode essential to the music, for, he who

gives a melody, ignorant of its mode, acts as does he who composes a syllogism in defiance of the

correct procedure and form.

(Allaire 1972, 62)

(italics original to Allaire's translation)

(cont. ...)

139

(and not only the description of their octaves, or referential steps, by means of Guidonian

syllables) has certainly additional consequences for solmization, other than the supposition

that they may influence the choice of mutation-steps. To be sure, there are modes that rarely

(or never) make use of the molle hexachord (i.e., that rarely have any in their melodies),

such as the tetrardus or deuterus modes, just as there are modes that more often use the

molle hexachord—such as the tritus and protus modes, especially in their arrangement as

autenticus modes—unless they are transposed.

However, it is not only the proper memory of the sound that has to be considered as

a mutation-factor, but also the deduction of the intervals surrounding the place of mutation

and the recognition of each hexachordal gesture. These must be carefully observed, and

since they might take a larger fraction of seconds to be perceived, the performer needs (or

needed) to adapt him/herself to each situation. Thus, the best places for mutation are also

those in which the score-reader can take time to conceive, aurally and rationally, the changes

of syllables and intervals, while committing to memory the previous sound. In light of these

considerations, two supplementary guidelines can be inferred. The third guideline is: if

possible, the reader may choose to mutate after a rest. Thus the step before the rest will be

solmized according to the previous hexachord, and the step after, according to the new

Spangenberg's text, clearly based on that of Ornithoparchus, elaborates further on the "rules of

mutation" and expands their number from twelve to eighteen items. One example of Spangenberg's

elaboration is given in the first item, above, in which he compares the so-called 'ignorance of the mode'

(during solmization) to a kind of defiant (or false, deceptive) "syllogismus" (or else a 'sophisma').

Rhetorical tools like this may cast a more pronounced speculative background on Spangenberg's work,

notedly differentiated from the works of both Ornithoparchus's and Lanfranco's, whose presentations are

aimed at more practical concerns.

140

hexachord. It seems safe to assume that this guideline holds true for rests that are not too

long (perhaps no more than one or two tempora), or the memory of the previous step could

be weakened. The appropriate length of the rest has to be considered in accordance with

each situation (melodic, rhythmic, or even harmonic), as well as adapted to the aural and

technical ability of each performer. The fourth guideline is: longer note-values allow more

time for mutation than shorter note-values. This suggestion arises as the logical converse of

Cochlaeus's and Rhau's statements on 'explicit' mutation. If an 'explicit' mutation cannot

happen in smaller note-values, it seems to be unequivocally feasible on longer note-values.

(Longer note-values, however, do not ensure the execution of an 'explicit' mutation, for it

imposes a solmization that would reinflect, rearticulate a single note: a result condemned by

the great majority of the theorists, unless the note is repeated.) Similar to what was said in

relation to rests, the appropriate length of the note-value is informed by the situation and

context of each single piece—it seems, however, that one should discard (as

places of mutation) note-values smaller than a minima (unless, perhaps, when it is a minima

alterata).

Hitherto, mutation has been presented only within the context of musica recta,

though all the concepts and guideline-suggestions above may be applied to musica ficta as

well. Nevertheless, before proceeding to more specific topics related to ficta, some practical

examples may help understanding solmization, and mutation exclusively within a

recta-context. In the following example (FIG . 3 .1), two distinct melodic gestures denote two

hexachords: the -hexachord (first gesture), and the -hexachord (second gesture).

141

8

: ut re fa fa sol fa reut ut

|

re=: =sol fa re

4 fa miut fa

4 sol fa fa mi ut rere ut

FIGURE 3 . 1 - Mutation from a -hexachord to a -hexachord.

In FIG . 3 .1 , the mutation may stand as an example for the first, second, third and

fourth guidelines given above. For instance, the one recta-step involved in the mutation

(d-la-sol-re) is uttered consecutively by means of two distinct syllables (re and sol); thus

constituting an 'explicit' mutation as described by Cochlaeus and Rhau and, since it is made

on a repeated note, agrees with the first guideline given above. In the melody itself, which

represents Mode 7, d-la-sol-re may be characterized as its 'dominans'—thus, a mutation on

the 'dominans' (agreeing with the second guideline). The two hexachordal steps involved in

the mutation (d-re and d-sol) are separated by a stroke indicating a caesura (i.e., a brief

pause); thus following the concept that a mutation (whether or not 'explicit') may benefit

from the presence of a pause (agreeing with the third guideline). At the same time, the

d-la-sol-re may be understood as a lengthened step, not only because of its repetition, but

also because it involves a natural prolongation at the last note of a plainchant-like phrase (as

indicated by the dot). It is a mutation that involves a longer note-value (agreeing with the

fourth guideline). The next three musical illustrations (FIGS. 3 .2 , 3 .3 , and 3 .4) are closely

derived from FIG . 3 .1 . All make use of the 'explicit' case of mutation (allowed by the

repeated d-la-sol-re), and their first melodic gesture is the same (naturally with the same

142

solmization). They differ, though, in the second melodic gesture, which introduces a few

melodic variations in the middle portion of the gesture (although it preserves the first step at

the beginning and the last six steps), and (in FIGS. 3 .3 , and 3 .4) also introduces the use of

ficta-signs within a recta-context.

8

: ut re fa fa sol fa reut ut

|

re=: =la mire ut remimi

3 remisol fa remimi re

FIGURE 3 . 2 - Mutation from a -hexachord to an -hexachord.

In FIG . 3 .2 , there are again two hexachords used in the solmization: -hexachord

(for the first gesture); and -hexachord (for the second gesture). Since an 'explicit' mutation

involves two distinct step-syllables being uttered on a unison, each solmization syllable is

represented in this dissertation as follows: the syllable pertaining to the first hexachord

(with an equals sign to its right side) is written above the first step; the syllable pertaining to

the second hexachord (with an equals sign to its left side) is written above the second

step—thus, the mutation is read re=sol in FIG . 3 .1 , and re=la in FIG . 3 .2 .104 Given the

104 In this dissertation, the following representation of a solmization has been adopted. First,

each hexachord is indicated by a capital letter (which indicates where the syllable ut would fall) framed by a

colon to its right side and two horizontal lines above and below (i.e., both an underline and an overline).

As explained briefly in chapter 1 (note 40), the resulting symbol is intended as a module pitch-letter

(similar to a number-module in the mathematical sense), through which no octave determination should be

understood (e.g., -hexachord indicates a hexachord whose ut falls on any C, in any octave). Second, a row

of solmization syllables is written above each step solmized according to that hexachord. Third, when a

mutation happens, the row of syllables of the second hexachord is not written on the same line (or layer) of

143

compass and intervallic configuration of the second gesture in FIG . 3 .2 , solmization should

naturally be made according to the -hexachord, which elicits the syllable fa on the b place

(producing a -fa—equivalent to modern b ), even though no fa-sign has been notated.105

The first gesture, however, allows for two different solmization options: one according to the

-hexachord (as indicated above), and the other according to the same -hexachord

employed for the second gesture (which shall be now discussed). If the -hexachord

solmization is adopted for the first gesture, three alternatives must be considered for the

actual solmization, since the four higher notes in that melodic gesture (f, f, g, f) lie outside

that -hexachord. First, at least the six initial notes would be solmized according to the

-hexachord (as ut fa, fa, sol, fa), and a mutation to the -hexachord would be made on the

seventh note (d-la-sol-re). This would constitute an 'implicit' (or 'mental') mutation, in

which d would be initially thought as re, but uttered as la. This first alternative seems

possible, but it would not benefit from the smoothness of an 'explicit' mutation and would

divide the first gesture in two parts. The -hexachord solmization would both preserve the

cohesiveness of the phrase at the solmization level and maintain a seamless transition to the

next phrase (not only because it would be an 'explicit' mutation, but also because it would be

a mutation made between phrases, where a hexachordal change can be less conspicuously

perceived). The second alternative would involve two recta -hexachords, an octave apart

the previous row of syllables (pertaining to the first hexachord), but rather one layer above. Fourth,

mutation-syllables always bear an equals sign (to the right side of the syllable pertaining to the first

hexachord, and to the left side of the syllable pertaining to the second hexachord).

105 By the same token, since the second gesture in FIG. 3 . 1 denotes a -hexachord solmization,

its bs are all -mis (equivalent to modern b ).

144

from each other: the solmization would start with the lower -hexachord (with the syllables

sol and la, for the first two notes); then proceed with the higher -hexachord (with the

syllables ut, ut, re, and mi, for the four higher notes); and finally returning to the lower

-hexachord (for all the remaining notes of the melody). However, this second alternative

would provide no common-step for mutation between the two -hexachords—that is, the

change from d-la to f-ut (second to third note), and back from f-ut to d-la (sixth to seventh

note) has no common-step and, therefore, no actual mutation can be made. The third

alternative would use the same solmization syllables suggested in the second alternative, but

applied to those four higher notes according to the concept of octave equivalence.106

Although octave equivalence needs no mutation to be implemented, and those four higher

notes show only two steps (f-ut and g-re), it seems excessive to impose that kind of

solmization concept upon forty percent of the first gesture. To be sure, octave equivalence

is proposed only for ephemeral step-occurrences with conspicuous octave references within

the main hexachord (in this case, within the lower -hexachord) implemented beforehand.

For all these reasons, it seems better to use only the -hexachord option for the solmization

of the entire first melodic gesture (as indicated in FIG . 3 .2).

Having illustrated these solmizations and related mutations, another two illustrations

(FIGS. 3 .3 , and 3 .4) will be presented, still working within a recta-only context, but with

intervening ficta-signs duly notated. In fact, the function of a ficta-sign is twofold: (a) a

ficta-sign may contradict a melodic gesture, by forcing the solmization into a different

106 According to what has been exposed in chapter 2 (iv).

145

hexachord than the one expected (the most common situation); or (b) it may serve to

elucidate the hexachordal solmization in an otherwise unclear or ambiguous melodic

gesture. In other words, ficta-signs are used to enforce syllables or to implement a

solmization according to a particular hexachord. This is in fact their true significance and

primary function, a 'solmization significance' that enforces a 'hexachordal function.' For

instance, on the one hand, if a is positioned on the staff-place of ee (equivalent to modern

e"), it will produce the solmization ee-fa, which can only pertain to the -hexachord (thus,

the resulting step is equivalent to the modern, inflected pitch e "). On the other hand, if a

is positioned on the staff-place of ff (equivalent to modern f"), a step that did not exist in

the a recta-gamut, then it will be ascertaining (to any note-shape falling on that place) only a

solmization as ff-fa, pertaining exclusively to a ficta -hexachord (but which is still

equivalent to the modern, non-inflected f"). Although ficta-signs may present a 'momentary

accidental function,' they cannot be identified with any accidental (in its modern context).

When they do enforce accidental-inflections, it happens only as a subsidiary consequence

(or byproduct) of hexachordal solmization, and not as a direct result of their significance or

primary function.

In FIG . 3 .3 below, the hexachords that frame the 'explicit' mutation are: the

-hexachord (first gesture) and the -hexachord (second gesture). Both gestures have the

same melodic outline presented in FIG . 3 .1 , except for the present of a fa-sign ( ) placed

immediately before the second gesture. In FIG . 3 .1 (with no ficta-sign), the second gesture

was solmized according to the -hexachord; in FIG . 3 .3 (with a sign enforcing a -fa), the

146

-hexachord is the one that must be solmized (since it is the only hexachord to which a -fa

can pertain).

8

: ut re fa fa sol fa reut ut

|

re=: =la sol mi

3 sol fa resol

3 la sol sol fa remimire

FIGURE 3 . 3 - Mutation from a -hexachord to an -hexachord, forced by a

ficta-sign.

In FIG . 3 .4 , there are two 'explicit' mutations, with three hexachords involved in the

solmization: -hexachord (first gesture); -hexachord (first part of the second gesture); and

-hexachord (second part of the second gesture). Both gestures have the same

melodic outline presented in FIG . 3 .2 , except for the presence of a mi-sign ( ) that divides

the second gesture in two distinct hexachordal parts. Although in FIG . 3 .4 the second

gesture initially requires an -hexachord, the mi-sign on the b-line (positioned between G-re

and a-mi) indicates a change in the intervallic configuration, and therefore that the

-hexachord can no longer be utilized, thus requiring a necessary mutation to accommodate

the -hexachord thereafter (the only hexachord that includes a syllable mi on the

b-position). The alternatives for appropriate place of mutation, in this situation, could be

chosen on any place before reaching the actual -mi, and after F-ut had been solmized (since

there is no correspondent syllable for the step-letter F within the -hexachord). The most

appropriate place is clearly where there is a note-repetition, immediately after the mi-sign,

147

producing a change of hexachord (an 'explicit' mutation) between a-mi (for the

-hexachord) and a-re (for the -hexachord), thus, mi=re. All of the other notes between

F-ut and -mi do constitute common-steps for the two hexachords, and could as well be

utilized in the mutation; but they must be discarded as secondary alternatives, since they

show no immediate repetition, allowing only an 'implicit' case of mutation.

8

: ut re fa fa sol fa reut ut

|

re=: =la mire ut remi=

: =re

4

ut refa mi ut rere ut

FIGURE 3 . 4 - Mutation from a -hexachord to an -hexachord, then to a

-hexachord forced by a ficta-sign.

Based on the last two examples above, and on the idea that the function of

ficta-signs is to enforce solmization-syllables and their correspondent hexachords,

a fifth guideline may now be inferred: a ficta-sign may serve to indicate the proximity of a

place of mutation, which can be done either after or before the actual position of the sign,

but must be done before the note whose syllable has been enforced (changed or confirmed)

by the sign—this applies whether the sign is a fa-sign ( ), or a mi-sign ( , or , or ). This

function of signs is well-attested in the Berkeley Manuscript, where three reasons for

implementing a mutation are enumerated.

148

Preterea fit triplici racione, scilicet racione

vocis, racione signi, aut racione utriusque

simul. Racione vocis quoniam ut est infima,

la vero vox suprema, ultra ut descendere et

ultra la ascendere, de quacumque voce nemo

potest nisi ea dimissa et locus eius inferiori

pro ascensu aut superiori pro descensu

assumpta. Racione signi fit quando

superveniens signum b seu # mutat incepti

cantus proprietatem [...]. Racione utriusque

fit propter nimium ascensum vel descensum,

una cum aliquo supervenienti signorum

dictorum.

(Anon. Berkeley 1375, tr. 1, ch. 2;

Ellsworth 1984, 48)

Further, this [i.e., a mutation] is done for

three reasons: by reason of the syllable, by

reason of the sign, or by reason of both

together. By reason of the syllable--since ut

is the lowest and la is the highest

syllable--no one from any syllable can

descend below ut or ascend above la unless

the syllable has been left and its place

assumed by a lower one for ascending or a

higher one for descending. By reason of the

sign, mutation occurs when the insertion of

the signs b or # changes the property

[proprietas] of a song that has already begun

[...]. By reason of both, mutation occurs

because of too great an ascent or descent

together with any insertion of the said signs.

(Ellsworth 1984, 49)

(interpolation and ellipsis mine)

The first item ("by reason of the syllable") refers to situations when a melodic

gesture reaches its limits (lower at ut, or higher at la). The second clearly refers to the use

of ficta-signs serving as indications (enforcers) of change between hexachords (or rather,

proprietas, since here the recta-context is the only basis for discussion). The third item

then establishes that both melodic gestures and ficta-signs can serve the same purpose:

defining hexachords and indicating the mutations. The next illustration (FIG . 3 .5)—an

excerpt in its original notation from a treatise by Guillaume Guerson [also called,

Guillermus Guersonus de Villalonga]—presents both 'explicit' and 'implicit' mutations, with

ficta-signs used for the definition of hexachords. Its arrangement follows the author's

descriptions for all mutations of each single recta-step, and shows the last mutation (re-sol)

that Guerson illustrates for g-sol-re-ut, followed by the first three mutations (la-mi, mi-la,

la-re) for aa-la-mi-re. These three are introduced by the words that run from the first to the

149

second staff, and read: "In a la mi re sunt sex mutationes" ("In [a]a-la-mi-re there are six

mutations").

FIGURE 3 . 5 - Excerpt from Guillaume Guerson's Utillissime musicales regule

([ca. 1495], ch. 3, f. b iiiir).

The first four notes in FIG . 3 .5 constitute the remainder of a gesture (which began

on the previous folio—f. b 3v) that denotes the -hexachord (ending on the syllable re),

followed by an 'explicit' mutation to the -hexachord (beginning on the syllable sol). That

gesture denoting the -hexachord (which ends on the syllable sol of g-sol-re-ut) is then

linked to the last gesture on the first staff, which again denotes the -hexachord. The

mutation between those two hexachords is made on a non-repeated note (thus an 'implicit'

mutation on the step aa-la-mi-re), in which the syllable la (pertaining to the -hexachord) is

only mentally conceived, and the syllable mi (pertaining to the -hexachord) is the one

actually uttered. The next change between hexachords is also an 'implicit' mutation,

indicated at the beginning of the second staff by the syllables mi (according to the

150

-hexachord) and la (according to the -hexachord), where mi is mentally conceived and la

is uttered. The last hexachordal change in the example is an 'explicit' mutation, in which the

syllable la (pertaining to the -hexachord) is solmized in the first gesture, and the syllable re

(pertaining to the -hexachord) is solmized in the second gesture. Notice that the compass

of the last melodic gesture ranges from g-sol-re-ut to dd-la-sol (only a fifth), which could

be an indication that either the - or the -hexachord should be taken for solmization. If the

melody was presented with regular notation (with no indication of syllables), and

considering that the previous solmization involved only the - and -hexachords, an

-hexachord solmization for that last gesture might have seemed appropriate. It is the

presence of the mi-sign ( ) that prevents any other solmization and enforces the

-hexachord, in accordance with Berkeley's second reason for mutation. Similarly, the

presence of the fa-sign ( ) in the first staff served as a clarification for the solmization of the

-hexachord, although the melodic gesture itself (whose compass ranges from f-fa-ut to

dd-la-sol) would be a sufficient indication for that hexachord, in accordance with the third

reason given by the Berkeley anonymous. In order to make these explanations clearer,

Guerson's illustration is transcribed below (FIG . 3 .6), with solmization-syllables for

each step, including those involved in the mutations presented in Guerson's treatise.

As attested in the quotations of Cochlaeus and Rhau above, an 'implicit' mutation is

executed on a single step by mentally conceiving the syllable of the first hexachord and

uttering the syllable of the second. Frequently, however, on the note that immediately

precedes the place of mutation, it seems appropriate to be already thinking (i.e., 'mentally

151

anticipating') the syllable of that second hexachord, while the last syllable of the first

hexachord is still being uttered.

ÚÄÄÄÄÄÄ¿: re mi fa

ÚÄÄÄÄ¿re=

: =sol mi re mi

ÚÄÄÄÄÄÄÄ¿ ÚÄÄÄÄ¿

fa sol [la=]: [=re]=mi fa

ÚÄÄÄÄÄÄ¿ÚÄÄÄÄ¿

sol fa la sol fa

ÚÄÄÄ¿ÚÄÄÄÄÄ¿mi ut re mi

ÚÄÄÄ¿fa [mi=]: =la mi

ÚÄÄ¿ÚÄÄÄÄÄ¿

fa re fa sol

ÚÄÄ¿ÚÄÄ¿

la=: =re mi fa sol

ÚÄÄÄÄ¿

mi ut re mi fa

ÚÄÄÄ¿

mi re

FIGURE 3 . 6 - Mutations ('explicit' and 'implicit') involving the three basic recta-

hexachords. Solmization syllables in boldface were given in the

source (Guerson [ca. 1495], ch. 3, f. b iiiir).

The 'implicit' mutation from the -hexachord back to the -hexachord (first staff) is

executed on aa-la-mi-re through the syllables la and mi (according to Guerson's

determination); nevertheless, the note before (g-sol-re-ut) could as well be used for that

mutation, notwithstanding Guerson's agenda to show a mutation (a first exchange of

syllables) on aa-la-mi-re. Therefore, it seems appropriate that the actual mutation on

aa-la-mi-re be anticipated by a virtual mutation on g-sol-re-ut, which is still being solmized

with the syllable sol (according to the -hexachord), but which can also support a

non-uttered (aurally conceived) syllable re (according to the upcoming -hexachord). On

the following 'implicit' mutation (second staff, from the - to the -hexachord), however, the

152

same anticipation cannot happen, for the step that immediately precedes the

place of mutation is -fa (which, as unanimously declared by the theorists, does not

constitute a proper step for mutation of any kind).107

In order to establish an appropriate nomenclature for the two syllables that are

always involved in any mutation, one may look into Rhau's propositions (also on p. 134).

Mvtatio musica, est vnius vocis in

aliam, in eadem claue, vnissona variatio, ob

vocum paucitatem et cantus pluralitatem

reperta, Ad quam duae necessariae sunt

voces. Vna dicitur mutata, quae per

mutationem relinquitur, Altera mutans, quae

loco vocis mutatae assumitur.

Est igitur duplex mutatio, Explicita, in

qua vox mutans et mutata ambae

exprimuntur, haec alio nomine vocalis

dicitur, Implicita siue mentalis est, in qua

vna vocum canitur et altera mente tenetur.

(Rhau 1517, ch. 3, f. C iir–v)

Musical mutation is [when] one syllable

[is made] into another, in the same

step-letter, [it is] a variation on the unison,

due to a paucity of syllables and to

conspicuous surplus of melody. With

respect to that, two syllables are necessary:

one is called "mutated" (mutata), which is

omitted in the mutation, and the other [is

called] "mutant" (mutans), which is adopted

in lieu of the mutated syllable.

Therefore, mutation is twofold: Explicit

(or Simple), in which both the mutant and

the mutated syllable[s] are articulated,

[where] one vowel is said through another

name; Implicit (or Intricate) or mental is

[that] in which one syllable is sung and the

other is kept in the mind.

(my translation)

As stated above, the first mutation-syllable should be called "mutated" ("mutata"),

and the second mutation-syllable should be called "mutant" ("mutans"). In his treatise,

Rhau applies this nomenclature to both 'explicit' and 'implicit' mutation—the former

107 In this dissertation, the following representations were adopted for the solmization of syllables

in the 'implicit' mutation. The first one (which is mentally conceived, not uttered) is represented by a

solmization syllable (with an equals sign to its right side) enclosed in square brackets—e.g., [re=], or [la=],

etc. The second one (which is actually uttered) is represented by a solmization syllable (with an equals sign

to its left side) that is not enclosed in brackets (just as the second syllable in the 'explicit' mutation)—e.g.,

=sol, or =mi, etc.

153

occurring when both syllables are uttered, and the latter occurring when the

'mutated'-syllable is dismissed and only the 'mutant'-syllable is uttered. (This dissertation

will follow the 'mutated'/'mutant' terminology suggested by Georg Rhau.)

In most historical treatises, the definitions given for mutation generally can be

identified with descriptions applied to the 'implicit' case, whereas descriptions based on the

'explicit' case are rarely suggested.108 Also, before Rhau's use of the terms "mutata" and

"mutans," there seems to have existed no consistent effort in creating an appropriate

terminology that could at once identify and define the function of each one of the syllables

involved in a mutation.109 Nevertheless, a few earlier theorists did employ descriptions and

explanations about mutation that could as well be taken as forerunners of the

'mutated'/'mutant' terminology, as in the case of the statements provided in the Berkeley

Manuscript—a slightly larger portion of the passage quoted here has also been quoted

earlier (cf. p. 149).110

108 Cf. above in the previous section and in the beginning of this section.

109 Apparently, Rhau was the first to consistently employ those terms, later used by other

theorists: Johann Spangenberg (1536, f. B5 r); Johann Vogelsang (1542, ch. 5, p. 26; Federhofer-Königs

1965, 87); Hermann Finck (1556, bk. 1, ch. [8]; f. E iiijv).

110 In fact, in the Berkeley Manuscript the explanation is more properly applied to 'transition'

("transitus") as a whole, which serves as description both to 'mutation' and to 'permutation.' In the

terminology used by the anonymous Berkeley author, the term 'permutation' is not used, but is described as

the process involved when one solmizes "through disjunct" syllables ("per disiunctas")—cf. (Anon.

Berkeley 1375, tr. 1, ch. 2; Ellsworth 48). The relevant passage will be quoted below in chapter 5 , whose

topic is 'permutation.'

154

Preterea fit triplici racione, scilicet racione

vocis, racione signi, aut racione utriusque

simul. Racione vocis quoniam ut est infima,

la vero vox suprema, ultra ut descendere et

ultra la ascendere, de quacumque voce nemo

potest nisi ea dimissa et locus eius inferiori

pro ascensu aut superiori pro descensu

assumpta.

(Anon. Berkeley 1375, tr. 1, ch. 2;

Ellsworth 1984, 48)

Further, this [i.e., mutation] is done for

three reasons: by reason of the syllable, by

reason of the sign, or by reason of both

together. By reason of the syllable--since ut

is the lowest and la is the highest

syllable--no one from any syllable can

descend below ut or ascend above la unless

the syllable has been left and its place

assumed by a lower one for ascending or a

higher one for descending.

(Ellsworth 1984, 49)

(interpolation and underline mine)

Although the above translation does not emphasize all the words that may have led

to later terminology, the text is clear in describing the function/character of each

mutation-syllable. Thus, the syllable pertaining to the first hexachord (the one preceding the

chosen step for mutation) is 'dismissed' (from "dimissa," instead of "left" in the above

translation). That is, the syllable is abandoned in order to make way for the new syllable

(and the correspondent hexachord) that will be enforced from the place of mutation onward.

As for the other, the syllable pertaining to the second hexachord (the one positioned

subsequently to the chosen step for mutation) would be assumed (from "assumpta"; lit.,

assumed, adopted, acquired). In other words, that second syllable is the one actually uttered,

denoting that a new hexachordal context is being adopted. However, in the Expositio manus

(p. 1477), Johannes Tinctoris presents a seemingly hybrid terminology between the one

appearing in the Berkeley Manuscript (1375) and the one employed in Georg Rhau's

treatise (1517).

155

[I]n omni mutatione fienda duae voces

requiruntur, scilicet una quae mutatur, et alia

quae per ipsam mutationem assumitur.

(Tinctoris p. 1477, ch. 7; Seay 1975-78, 2:

52; CS 4: 10, 12)

[T]wo syllables are required in every

mutation about to be made (fienda), namely

one that is mutated, and another that is

assumed [i.e., adopted] through the mutation

itself.

(my translation)

Although the translation is similar to Rhau's 'mutated' (for the first syllable) and the

Berkeley anonymous's 'assumed' (for the second syllable), Tinctoris uses the passive verb

forms "mutatur" and "assumitur," whereas Rhau and the Berkeley anonymous author use

verbal adjectives (which are more suitable to becoming a direct foundation for terminology

than a verb per se). In any case, one wonders what could have been the reason not to take a

pair of terms such as 'dismissed'/'assumed' as an appropriate reference (or description) for

those mutation-syllables, and create a different pair such as 'mutated'/'mutant.' Perhaps the

reason might be found in the Latin form itself ('mutata'/'mutans'), which seems to refer to

the maxim 'mutatis mutandis' ('having changed what should have been changed,' or 'all

necessary changes having been made'). As a legal qualification, this adverbial phrase can be

applied, for example, to argumentations that seek the validation of a contract in which some

items have been changed, like in a definition-phrase such as: 'what has been changed

for/from a first situation must to be observed, in order to inform and allow correspondent

changes in the second or in the remainder of the situations.' However, these changes

usually do not involve a change in the actual text of contractual clauses, only in the

associated data that may serve to clarify an interpretation or to contextualize a legal

contract—i.e., without changing significative parts of its content, but which may alter some

156

of its context (thus, a change that keeps the integrity and coherence of the text).111 In a

comparison with mutation, the text of a contract may be taken as the notated melody itself,

and the context as the set of deduced hexachords—thus, the above definition-phrase may be

paraphrased to fit a musical context by substituting 'hexachord' or 'syllable' for 'situation.'

Finally, this section must deal with yet another case, or rather sub-case of 'implicit'

mutation. As it has been defined above, an 'implicit' is realized when the 'mutated'-syllable is

mentally conceived, while only the 'mutant'-syllable is the one actually uttered. Nevertheless,

there is a possibility of having the utterances inverted, or even having the both syllables

omitted—in either of the two situations what is significant, in fact, is that the

'mutant'-syllable is only mentally conceived. The denomination for this sub-case shall be

'indirect' mutation, since the actual utterance of syllables pertaining to the new hexachord is

obtained only after the actual place of mutation. The situation in which both utterances are

omitted is one that takes place on a rest, between two distinct melodic gestures—as

illustrated above in the mutation between the -hexachord and the -hexachord in measure

57 (in the motetus part) of FIG . 3 .7 . In this 'indirect' procedure on a rest, both the 'mutated'

and the 'mutant' syllables should be solmized either according to the step before the rest, or

111 In the Black's Law Dictionary, the following sentence is given as an example: "what was said

regarding the first contract applies mutatis mutandis to all later ones." In modern contracts, for example,

this would apply to simple changes of address, telephone number, or even addition or suppression of parties

without changing the text or merit of a contract itself—cf. (Webster's 3e, s.v. 'mutatis mutandis'; Graves

2003, s.v. 'mutatis mutandis,' http://www.jurisdictionary.com/dictionary/dictionary%20m.html; Dall'Oca

and Santana 2004, 113, s.v. 'mutatis mutandis'; Garner 2004, 1044, s.v. 'mutatis mutandis').

157

according to the step after the rest, in order to create the proper aural reference for the

hexachordal change.

[Motetus]

3

(fa)-cun -di –

: fa mi re

[Tenor]

: sol

[55]

mi

mi

mox

[mi=: =sol]

sol

lu

fa

3 fa

5

–

mi

mi

5

pi–

mi fa

FIGURE 3 . 7 - 'Indirect' mutation on a rest (both syllables are not uttered).

Excerpt from "Garrit gallus—In nova fert—[Neuma],"

mm. 54–60—(F-Pn fr. 146, f. 44v).

The other situation, in which only the 'mutant'-syllable is mentally implied, can itself

occur either as a virtual approach or as a definite approach. The former is here interpreted

as an anticipated mutation alternatively conceived on the step that precedes the true

place of mutation. This virtual approach has been illustrated in FIG . 3 .6 for the step

g-sol-re-ut, which (in that function) precedes the actual mutation between the - and the

-hexachords that takes on aa-la-mi-re. The latter instance may happen when the omitted

utterance of the 'mutant'-syllable seems to be the fitting approach, in face of two

circumstances: the 'mutant'-syllable has been obtained by means of the ephemeral

octave-equivalence resource; and the sound of the step that follows the place of mutation has

158

been aurally ingrained (usually by means of a prior reiteration) in the mind of the performer,

and thus may dispense with the certainty of an intervallic reference with the previous

step—although these circumstances may happen separately, in order to better characterize

the 'indirect' mutation they should be concurrent.

! 8

: ut mi sol fa mi 3

ut=: =sol la mi fa mi ut re=

: [=sol]mi re ut

FIGURE 3 . 8 - 'Indirect' mutation on a note (only 'mutant'-syllable is not uttered).

This definite approach is illustrated in FIG . 3 .8 , showing two mutations: the first,

from the -hexachord to the -hexachord, is an 'explicit' mutation that takes place on the two

consecutive step-letters c (from the 'mutated'-syllable ut, to the 'mutant'-syllable sol); the

second, back from the -hexachord to the -hexachord, is the 'indirect' mutation on the

single step-letter g, (from an uttered 'mutated'-syllable re, to a non-uttered 'mutant'-syllable

sol). Notice that in whatever instance (virtual or definite) of a non-uttered 'mutant'-syllable,

the 'indirect' mutation will happen on a single step whose importance is notably greater in

the first ('mutated') hexachord than in the second ('mutant') one. Mutations of other species

and types will be inspected in the next chapter, together with indications for hexachordal

changes promoted by ficta-signs according to their position.

159

— CHAPTER 4 —

MUTATION:IRREGULAR TYPE, FICTA-SPECIES, AND POSITION OF FICTA-SIGNS

Most of what has been explained above regards only 'regular' mutation within a

recta-only environment, hence the present section will undertake the presentation of two

other kinds of mutation: 'irregular' mutation (mutatio irregularis), and mutation involving

musica ficta or 'ficta-mutation' (or falsa mutatio, as some authors preferred). In fact, these

two kinds are not established according to the same parameters, nor are they paired as

opposites: the 'irregular' type is opposed to 'regular' type of mutation, and the 'ficta' species

is rather opposed to the 'recta' species of mutation. A ficta-mutation happens when at least

one of the mutation-syllables (sometimes both) generates a ficta-step where it is applied

(denoting the use of a ficta-hexachord); whereas a recta-mutation happens only when both

of the mutation-syllables denote the use of recta-steps (i.e., of steps pertaining to one of the

three basic hexachords). Thus, the parameter that differentiates a ficta-mutation from a

recta-mutation is established according to the gamut-quality of the step (whether a ficta- or

a recta-step), relatively to each of the mutation-syllables ('mutated' and 'mutant'). In relation

to the 'regular' versus 'irregular' opposing pair, there are two parameters to be considered: (a)

the hexachordal subset in which each mutation-syllable is found (either the lower ut, re, mi

160

subset, or the upper fa, sol, la subset); (b) the melodic motion (either ascending or

descending) that follows the second ('mutant') syllable.112 If one of the mutation-syllables

is found in the lower subset, and the other is found in the upper subset, then the type

executed will be qualified as a 'regular' mutation.113 If both mutation-syllables are found in

the same subset (either the upper of the lower), then the type will be qualified as an

'irregular' mutation. If, however, the mutation-syllables were individually found in different

subsets, but the melodic motion after the second ('mutant') syllable was unusual (either

contradicting its position in the higher subset by proceeding through an ascending motion,

or contradicting its position in the lower subset by proceeding through a descending

motion), then the mutation would also be qualified as 'irregular.'114 Notice that when the

'regular' and 'irregular' types are considered in relation to the 'recta' and 'ficta' species of

mutation, they will serve as elements that determine four different subspecies: two

subspecies for the recta-mutation (regular recta and irregular recta), and another two for the

ficta-mutation (regular ficta and irregular ficta)—each of which being implemented

112 These two parameters (a) and (b) have been briefly explained on p. 131.

113 In the previous chapter, the 'regular' type can be found in all the mutations of FIGS. 3 . 1 –3 . 3

and FIGS. 3 . 5 –3 . 6 , and in the first mutation (from the - to the -hexachord) of FIG. 3 . 4 .

114 An 'irregular' type (both by the melodic motion parameter, and by the subset parameter) can be

found in the second mutation (from the -hexachord to the -hexachord) of FIG. 3 . 4 . The change is made

between syllables of the same subset (from mi of the -hexachord to re of the -hexachord), and the second

syllable (re) is followed by a descending melodic motion (even though it should be ascending).

161

according to one of the two cases (explicit or implicit) that depend on the presence or

absence of note-repetition for the proper place of mutation.115

As seen in previous sections, most theorists presented only generic definitions for

mutation (based mainly on parameters that would imply the 'regular' and 'implicit'

mutations) and did not discuss what happens when those conditions were not followed.

Most theorists also did not discuss ficta-mutation extensively, generally limiting their

presentations to statements that a ficta-mutation is one that involves the use of ficta-steps.

In the case of 'irregular' and 'explicit' mutations, this imprecise discourse is probably

justified by the relative scarcity of melodic situations that call for those mutations, whether

within the limits of musica recta, or even when ficta-hexachords were involved. In the

remainder of this section, the 'irregular' type and 'ficta' species of mutation shall be

individually illustrated and discussed according to their definition-parameters.

First, it seems that the melodic-motion parameter may be explained by the following

statement: when one ascends from one hexachord into another, it is highly probable that the

mutation will involve the higher steps (and syllables) of the first (lower) hexachord and the

lower steps (and syllables) of the second (higher) hexachord. Conversely, when the melody

descends, most likely the mutation will be done from the lower steps (and syllables) of the

higher hexachord, into the higher steps (and syllables) of the lower hexachord. However, in

their explanations theorists rarely referred to this melodic-motion parameter in the sense of

115 The nomenclature of species, subspecies, types, and cases of mutation has been devised in this

dissertation for the sake of differentiating clearly between its various structural levels, although there are no

historical treatises that have made use of any of those terms.

162

higher and lower hexachords, for their presentations were usually concerned with intervals.

Their main focus was not with the macrostructure of hexachords (or even modes), but with

the more detailed microstructure of intervals.

Maximillian Guillaud, in his Rudiments de musique practique (1554), presents a set

of three rules that appear to discuss mutation in terms of hexachordal motions, even though

his references to the three basic hexachords ( , , and ) are somewhat oblique, implied in

the generic designations of their proprietates ("nature," " dur," and "b mol"). The

quotation below shows the second and third rules presented in chapter 6 ("De

muances"—"On mutations"), from the first part of Guillaud's treatise.116

Seconde Reigle.

Pour monter de nature en dur ou de b mol

en nature, faut tousiours chanter re apres sol:

Et pour monter de dur en nature, ou de

nature en b mol, faut chanter re apres fa.

Troisieme Reigle.

Pour descendre de b mol en nature, ou de

nature en dur, faut tousiours chanter la

apres fa: Et pour descendre de dur en nature,

ou de nature en b mol, la apres mi.

(Guillaud 1554, tr. 1, ch. 6, f. A iiijr-v)

[Second rule.]

In order to ascend from the hexachord

naturale into the durum, and from the

hexachord molle into the naturale one must

sing re after sol; and in order to ascend from

the hexachord durum into the naturale, and

from the hexachord naturale into the molle

one must sing re after fa.

[Third rule.]

In order to descend from the hexachord molle

into the naturale, and to descend from the

naturale into the durum one must sing la

after fa; and in order to descend from the

hexachord durum into the naturale, and from

the naturale into the molle one must sing la

after mi .

(Allaire 1972, 48)

116 In his work entitled The Theory of Hexachords (1972), Gaston Allaire translated these same

rules from Guillaud's treatise, but presented them as "RULE V" and "RULE VI," respectively; the corrected

numbering is enclosed in square brackets in the quotation below.

163

Although his explanations may be applied to understanding 'irregular' mutation,

Guillaud's presentation is designed to explain only the 'regular' type. Guillaud defends that

a 'mutant' syllable should always be solmized re when in ascending motion and should

always be solmized la when in descending motion. Another statement defending that a

'regular' mutation should be effected only by means of the syllables re and la can be seen

in Hermann Finck's third rule of mutation.

III. In mutatione utimur duabus fere

uocibus, in ascendendo re, in descendendo la.

(Finck 1556, bk. 1, f. E iiijv)

(3) In mutation we generally use two

syllables: re in ascending [motion], la in

descending.

(my translation)

But in the context of his defense for re and la, Guillaud was referring exclusively to a

mutation between adjacent hexachords in relation to a circle of fifths—that is, only from the

- to the -hexachord, or vice versa, and from the - to the -hexachord, or vice versa.

Rounding off Guillaud's set of three rules on mutation, this context is clarified by his first

rule, quoted below.

Premiere Reigle.

Iamais proprement ne se fait muance de

b mol en dur, ne de dur en b mol, mais

tousiours de l'un des deux en nature, ou de

nature en l'un des deux.

(Guillaud 1554, tr. 1, ch. 6, f. A iiijr)

[First rule.]

It is never proper to the nature of the

hexachords molle and durum to be

interlocked; rather, the interlocking must be

made between the hexachords molle and

naturale, and between the hexachords naturale

and durum.

(Allaire 1972, 47)

Guillaud establishes that a mutation between - and -hexachords is 'improper' (or

rather "jamais proprement"—"never properly [made]," virtually a synonym of 'irregular'),

since it would risk dealing with both -fa and -mi as individual steps in the same melodic

164

gesture, or else with tritones (either melodically or harmonically).117 Taking again " -dur"

and "b-mol" as determinants of the durum -hexachord and the molle -hexachord,

Guillaud expands on the concept (already stated by earlier theorists) that no mutation can

occur on the double-step -fa / -mi and provides a qualification (or restriction) of 'irregular'

(or 'improper') to any mutation between those two hexachords. Such a definition clearly

adds another parameter for 'irregularity' (mutation between nonadjacent hexachords),

distinct from the other two (hexachordal subsets of syllables, and the melodic motion after

the 'mutant' syllable).118 Among Renaissance theorists there seems to have existed a

tendency toward restrictions, usually discussing no more than one of these parameters.

However, the tendency in medieval (and early Renaissance) treatises was to provide

definitions that considered a 'greater' number of parameters. In any case, only a few

treatises (either from the Renaissance or the Middle Ages) provided conspicuous references

or definitions of 'irregular' mutation.

Jacobus Leodiensis (Jacques de Liège) was possibly the first theorist to discuss

'irregular' mutation in greater detail, formulating five different meanings set by means of

117 Gaston Allaire's translation (used in the quotation of Guillaud's first rule on mutation) is again

misnumbered, he presents it as "RULE IV."

118 Andrew Hughes, in his entry on 'solmization,' has asserted that Jacobus Leodiensis

"maintained that mutation from hard to soft hexachord, or vice versa, was rare" (NG 1, 17: 460; NG 2e,

s.v. 'Solmization,' § I.3). However, there seems to exist no clear and coherent statement in Leodiensis's

treatise that could endorse such an understanding. In fact, he does seem to allow for a change between these

hexachords as a 'regular' mutation, as can be seen in his chapter entitled "De vocum inter se regularibus

mutationibus" ("On regular mutations of the syllables between themselves")—cf. (Leodiensis p. 1330,

bk. 6, ch. 65; CS 2: 289–292; Bragard 1955–73, 6: 179–184).

165

distinct parameters: (1) both mutation-syllables drawn from the same hexachordal subset,

with steps maintained within the limits of the recta-gamut (i.e., an recta-mutation of a truly

'irregular' kind); (2) use of ficta-syllables without altering the actual sound of a

correspondent recta-step (i.e., a mutation that involved ficta-steps whose syllables did not

impose any chromatic inflections on the recta-steps that shared the same step-letter); (3) use

of sudden (and momentary) steps extraneous to the hexachord under actual solmization

(e.g., as in the creation of an upper or lower leading-note to the last note of a final or internal

cadence); (4) use of fa and mi as mutation-syllables, but involving a change in the actual

sound on the same step-letter, as it is proper of the intervallic difference between these

syllables (i.e., a change of syllables with a chromatic pitch inflection); (5) a melodic gesture

that involved leaps of sixth, seventh, and octave with no actual mutation being realized—cf.

Leodiensis's Speculum musicae (p. 1330, bk. 6, chs. 66–69; CS 2: 293–302; Bragard

1955–73, 6: 183–199). Among all these meanings, the first is the only one that refers to

'irregular' mutation (according to the definition for that term adopted in this

dissertation)—although only a particular instance of it, a subspecies: a recta-only, 'irregular'

mutation. The second meaning refers to a ficta-mutation (discussed below in this section,

according to the terminology adopted in this dissertation), whether it is constituted by the

use of one ficta-syllable and one recta-syllable, or constituted by the use of two

ficta-syllables.119 The third meaning refers to what I am calling 'transmutation' (see chapter

119 For the purposes of and definitions adopted in this dissertation, it suffices to have just one

syllable of a ficta-hexachord (among the two mutation-syllables) for the qualification of a ficta-mutation.

Also, although Leodiensis is referring only to ficta-steps that are unison with recta-steps, a new syllable

166

6). The fourth meaning refers to what I term 'permutation' (see chapter 5), which is also

related to melodic and harmonic conflicts (and false relations) that involve either the

consecutive or simultaneous use of the syllables mi and fa.120 The fifth meaning is

presented here:

Dicunt autem aliqui mutationem irregularem

esse cum est processus supra vel infra

immediatus ad sextam, septimam vel

octavam vocem.

(Leodiensis p. 1330; Bragard 1955–73, 6:

186; CS 2: 293)

Moreover, some [people] say [that] irregular

mutation occurs, when [the gesture] proceeds

(est processus) immediately to the sixth,

seventh, or eighth syllable above or below

(i.e., by leap).

(my translation)

Jacobus refers here to a melodic situation that is usually taken by theorists and performers

as definite signs of mutation, since those intervals (sixth, seventh, and octave) exceed the

limits of any hexachord. The amalgam of meanings presented by Leodiensis seems to

reflect a conservatism to which he may have partially subscribed (or perhaps taken as a

(appended to a recta-step) may or may not impose a chromatic inflection—e.g., c-re in the -hexachord

does not impose any change of sound (i.e., no chromatic inflection) with c-sol-fa-ut (both being equivalent

to modern c'); but c-mi (equivalent to modern c ') in the -hexachord does impose an inflection. In the

adopted meaning here, ficta species serves as much for the presence of a ficta-step that finds a correspondent

unison with some recta-step, as for the presence of a ficta-step that imposes chromatic inflections. The

difference may also refer to distinct procedures of change when those steps are placed consecutively: the

former (in a unison situation) would be called a ficta-mutation, the latter (in an inflected situation) would

involve a ficta-permutation, except if the two steps are -fa and -mi (or their upper octaves).

120 The solutions to these conflicts are related to the so-called mi-contra-fa 'rule' or 'prohibition,'

whose concept is that a mi cannot be solmized against a fa when the notated interval between them

delineates a perfect consonance (diapason, diapente, and in some situations also the diatessaron), whether

directly or indirectly, without introducing a dissonance. As will be inspected later, some authors (esp. in

the Renaissance) even considered its application on imperfect consonances, although not all authors

followed this latter idea. Although mi-contra-fa is frequently related to harmonic situations (and may even

apply to indirect situations in which 'false-relations' need to be prevented), melodic situations may also

apply, especially in direct leaps, and sometimes in indirectly outlined consonances (i.e., when a consonance

is mediated by other steps).

167

foundation to support his own discourse). More likely, at that time most of the procedures

of solmization were only beginning to receive attention as independent concepts, he included

all of their meanings under the same umbrella. As discussions about music became more

and more specific, theorists began to discuss the procedures of solmization individually,

elaborating their definitions both for the sake of instructing the readers and to providing an

appropriate nomenclature for further discussions. Most of those theorists, however, did not

discuss ficta-mutation at length (and sometimes not at all). They often made only brief or

oblique references to it, sometimes classifying it as a subtype of 'irregular' mutation (as

mentioned above among the five different meanings given by Jacobus Leodiensis).121

Vocatur autem irregularis mutatio "falsa

mutatio" propterea quia vox mutatur in

vocem quae sibi non vere, sed false

coniungitur; vocatur etiam falsa musica, quia

vadit contra regularem vocum in gammate

<dispositionem>.

(Leodiensis p. 1330, bk. 6, chs. 66; Bragard

1955–73, 6: 185; CS 2: 293)

Now, irregular mutation is called 'false

mutation,' on the very account of a syllable

[that] is mutated into [another] syllable,

which is not itself truly, but falsely put

together [i.e., when a syllable is mutated

into a ficta-syllable, and not into a

recta-syllable]. Indeed, it is called falsa

musica, because it goes against the regular

arrangement of syllables in the gamut.

(my translation)

Although Leodiensis gives ficta-mutation (or falsa mutatio) only as a particular kind

121 Jacobus Leodiensis is again one of the first few theorists who have provided a somewhat

detailed discussion on the topic of ficta-mutation through the use of terms such as falsa mutatio and

irregularis mutatio.

168

of 'irregular' mutation, he may also be considered a theorist who provided one of the first

few detailed discussions on this topic.122 The concept of ficta-mutation also involved a

great amalgam of meanings, which vary from epoch to epoch or even from theorist to

theorist. In fact, since a ficta-mutation occurs only when the ficta-realm is involved, the term

falsa mutatio (or any other term with a similar meaning) was also used as a synonym for

musica ficta itself. A ficta-mutation can be made in two situations: between two

ficta-syllables, or between a recta-syllable and a ficta-syllable.

[Superius]

C'est ma-da -

: sol ut mi :

me qui

[sol=]=ut fa mire

:

par son

[ut=]=la sol

doulx re -

fa mi

gart

re

FIGURE 4 . 1 - Recta-mutation and Ficta-mutation. Excerpt from "Navré je sui

d'un dart pénétratif" (refrain, second part), rondeay by Guillaume

Du Fay—(GB-Ob, MS. Canon. Misc. 213, f. 78v; cf.

[transcriptions] Besseler 1964, 56; K.Berger 1987, 178).

In the first situation, the solmization must involve a change between two

ficta-hexachords, while in the second situation it must always involve one ficta-hexachord

and one of the three basic recta-hexachords ( , or , or ). FIGURE 4 .1 illustrates the latter

122 With regard to the nomenclatures applied to mutation, the terms 'irregular' (or 'improper') and

'ficta' (or 'falsa') were gradually presented with independent definitions, even if such an independence did not

happen thoroughly within the writings of Leodiensis.

169

situation in its second mutation (from the -hexachord to the -hexachord).123 The first

mutation shown above (from the -hexachord to the -hexachord) is a 'regular'

recta-mutation (of the 'implicit' kind) on the fourth note. The second mutation is a 'regular'

ficta-mutation (also of 'implicit' kind), in which a 'mutated' recta-syllable (represented above

by the symbol [ut=], according to the -hexachord) is replaced by a 'mutant' ficta-syllable

(represented above by the symbol =la, according to the -hexachord).124 This latter

hexachord is deduced in face of the fa-sign placed on the line of e (between the words "son"

and "doulx"), generating the ficta-step e-fa (equivalent to modern e '), which can only

pertain to a hexachord whose ut is placed on the ficta-step -ut (equivalent to modern b ,

and unison with the recta-step -fa). Thus, the situation involving a change from a

recta-hexachord to a ficta-hexachord will occur when a melodic gesture has moved away

from the realm of those three basic recta-hexachords, due to the presence of a ficta-sign

enforcing the ficta-hexachord (which will often, but not always, denote modern accidental

inflections), or due to a modal transposition (momentary or not).125 In relation to most of

123 Guillaume du Fay's rondeau Navré je sui d'un dart pénétratif has been discussed by Karol

Berger (1987, 177–188), detailing his readings of musica ficta. He also has included a full transcription of

that polyphonic song, together with facsimiles of the three extant copies contained in the following

manuscripts: GB-Ob, MS. Canon. Misc. 213, f. 78v; F-Pn, nouv. acq. fr., 6771, f. 98r; D-Mbs, Clm.

14274 (olim Mus. 3232a), f. 96r.

124 This second mutation in FIG. 4 . 1 is exactly the kind of ficta-mutation (i.e., falsa mutatio)

described by Leodiensis as a subtype of 'irregular' mutation: a change between two unison steps of different

species (a recta-step g-ut, and a ficta-step g-la).

125 Remember that the presence of a ficta-sign may or may not signify, in modern terms, the

corresponding presence of an accidental inflection. For example, in the case of a mi-sign, if it is positioned

in the place of b, the effect created will only produce the solmization of -mi (equivalent to the modern

170

the medieval repertoire and to some of the Renaissance repertoire, however, mutations

between two ficta-hexachords are likely to occur less frequently than mutations between a

recta-hexachord and a ficta-hexachord, since chromaticism and modal transposition are

more easily observed in the repertoire from the mid-Renaissance onward.126 The next

illustration (FIG . 4 .2) shows two ficta-mutations: the first one between a recta-hexachord

and a ficta-hexachord, and the second between two ficta-hexachords. In the first phrase, the

solmization of the -hexachord is given by the intervallic span of the melodic gesture,

together with the presence of a fa-sign indicating the recta-step -fa.127 Between the first

and the second phrases, another sign enforces the solmization fa on the step-letter E, which

(just as in FIG . 4 .1) calls for the solmization according to the -hexachord. In the third

non-inflected b ); but the positioning of a mi -sign in the place of virtually any other step-letter might be

seen as a sign that generates an accidental inflection in the modern sense. Also, in the case of a fa-sign, a

modern accidental inflection will happen often, even when it is applied to a b, generating the step -fa

(equivalent to modern inflected b ); however, the same does not happen, for example, when the sign is used

to indicate the ficta-step ff-fa (for which a fa-sign is considered necessary)—the exception to this need being

found only in the evidence of a few theorists that eventually included that step in their recta-gamut, mainly

from the fifteenth century onward, although in general there is no clear individual or group of scribes that

followed their precepts. In any situation, whether there is a chromatic inflection or not, ficta-signs do not

ensue the solmization of ficta-steps, for at least -mi and -fa (as well as -mi and -fa) are considered as

recta-steps by most theorists.

126 Of course, no historiographic division, nor stylistic definition can be made as watertight, or as

obdurate, which would be to say that chromaticism and modal transposition did not occur before that time.

127 Notice that it is not necessary to notate the -molle sign at the beginning the gesture, since

the configuration of the intervallic span already indicates the -hexachord. However, in its signature-like

position, that sign serves the additional purpose of indicating that the solmization for the entire passage

should be based mainly on hexachords pertaining to the molle family (i.e., to the molle proprietas). The

function of signs in signature positions will be briefly addressed in chapter 8 .

171

phrase (second staff), the ficta-sign denotes the presence of the ficta-step a-fa, and the

corresponding use of the ficta -hexachord.

3 3 : ut re fa fa

3 sol fa re ut ut

|

re=: =la sol mi sol

3 fa re sol la

|

3 sol=

: =re mi ut fa

3

la sol fa mi ut re

FIGURE 4 . 2 - Ficta-mutations (from a recta -hexachord to a ficta -hexachord,

and from a ficta -hexachord to a ficta -hexachord).

In both situations, the ficta-signs mark the place of mutation (that is, the point from

which a new hexachordal solmization should be understood), but they do not indicate the

exact step in which the mutation must occur, since that will be decided by parameters that

allow the change to be made as smoothly as possible, such as: (a) clear aural perception of

the step of mutation; (b) occasional note-repetition that might be used for the

step of mutation; (c) importance of step of mutation in the modal structure of the piece

and/or of the melodic phrase; (d) the possibility of realizing a 'regular' mutation instead of

an 'irregular' mutation (with regard to the use of syllable subsets, and the melodic-motion

that follows the mutant syllable); or even (e) the possibility of using the syllable re for the

172

mutant syllable followed by an ascending motion, or the syllable la for the mutant syllable

followed by an descending motion (at least considering, in this latter item, the restrictive

instructions given by Guillaud, Finck, and mainly other sixteenth-century theorists). In the

case of both mutations in FIG . 4 .2 , the note-repetition is one of the most important factors

for deciding on the proper place of mutation, although all the others have been duly

considered and satisfied, for both ficta-mutations are 'explicit' and 'regular.' The

determination of the species of mutation (recta or ficta) is completely dependent on the

presence of a ficta-sign, for in its absence the solmization is most likely to stay only within

the realm of the three basic recta-hexachords. The remainder of this section will investigate

the functions of ficta-signs with regard to solmization, to mutation in general, and to

ficta-mutation in particular.

First, as it has been repeatedly stressed above, the presence of a ficta-sign does not

necessarily ensure a solmization of ficta-hexachords, since under certain circumstances it

might serve only as an enforcer for mis or fas of recta-hexachords.128 It is also

conceivable that ficta-signs might be used to indicate other recta-steps than just -fa and

-mi (or their upper octave), usually for the sake of clarifying the proper solmization of a

melodic gesture, or to alter a ficta-context back to the recta-context. For instance, this is the

case for mi-signs applied to a-la-mi-re or e-la-mi (or their recta-octaves), or fa-signs

applied to c-sol-fa-ut or f-fa-ut (or their recta-octaves)—since they are steps that already

include those syllables in the recta-gamut (a-mi, aa-mi, E-mi, e-mi, C-fa, c-fa, cc-fa, F-fa,

128 Cf. FIGS. 2 . 5 , 2 . 7 –2 . 8 , 3 . 3 –3 . 6 , 4 . 2 . For other explanations, see also note 125.

173

f-fa) and therefore cannot be modified into ficta-steps by the solmization of the syllables mi

and fa prescribed by the apposition of the correspondent ficta-signs. Andreas

Ornithoparchus presents one musical example in which ficta-signs are being used not only

in order to indicate recta-steps (with mi- and fa-signs), but also ficta-steps (with fa-signs).

His example illustrates the third "Of the general rules of counterpoint" ("De generalibus

contrapuncti preceptis") in his treatise, whose text is quoted below with a translation by

John Dowland and with facsimiles of the example in the original notation (FIG . 4 .3 and

FIG . 4 .4). Ornithoparchus suggests that conspicuous intervallic conflicts between tenor and

the bass must be resolved into valid consonances (those are labeled "Basis valens").

Otherwise the bass itself will be considered incorrect, or invalid ("Basis non valens").129

Tertia, In concordantijs perfectis, nunquam

ponatur vox mollis contra duram: nec e

contra. Sed aut mollis contra mollem, dura

contra duram, aut saltem naturalem.

Naturales nanque ancipites, et cum b

mollibus et cum 5 duralibus concordabunt,

hoc modo.

(Ornithoparchus 1517, bk. 4, ch. 4, f. L iv)

3 In perfect Concordances neuer set a sharpe

Voyce against a flat, nor contrarily, but set a

Sharpe against a Sharpe; a Flat against a

Flat, or at least against a naturall. For the

Naturals are doubtfull, and will agree with 5Dures, and 3 Mols , thus?

(Dowland 1609, 80–81)

FIGURE 4 . 3 - Example in Ornithoparchus's original text.

129 The text is referring to the so-called mi-contra-fa conflict.

174

FIGURE 4 . 4 - Example in Dowland's translation.

The solutions are given in terms of inadequate or adequate pairing of ficta-signs

between the voices, which indicate, in fact, inadequate or adequate pairing of solmization

syllables (not accidentals, and with no concern to whether the necessary steps pertain to the

recta or to the ficta species). Therefore, it is noticeable that, although this is a problem

assigned to a chapter on counterpoint (a subject characteristic of musica speculativa

discussions), the text demonstrates a practical method of presentation (not a speculative

one). This may be seen as evidence of a concern with the prosaic activity of the performer,

rather than the specialized, highly learned activity of the composer or the theorist.

In order to facilitate this assessment, a transcription of the Ornithoparchus's musical

example is given below as FIG . 4 .5 . The tenor presents bs solmized only to the syllable fa;

i.e., true recta-steps indicated by the ficta-sign placed on the signature-like position. The

invalid bass-solutions clearly present mi-signs ( in the original notation, in the modern)

indicating the recta-steps E-mi and B-mi, while the valid bass-solutions present fa-signs

( in the original notation, in the modern) on the same step-places, generating their ficta

counterparts E-fa and B-fa.130

130 Although most musical examples from Ornithoparchus's original are reproduced in Dowland's

translation, there are occasional corrections and variants. With regard to this particular example, the second

mi-sign is clearly placed on the line of B (in the translation), while it is placed on the line of D (in the

175

8

3 : ut fa

Invalid bass.

4 : fa mi

3 mi fa re re

4 [ ]

fa /:/ mifa=

: =sol

ut

ut

8

3 : ut fa

Valid bass.

3 : sol fa

3 mi fa rere

3 sol [ut=]

: =fa sol

ut

ut

FIGURE 4 . 5 - Functions of ficta-signs (indications of recta- and ficta-steps and

correspondent mutations).

Notice also that, in the invalid bass-solution, there is no possible mutation between

the third note (F-fa) and the fourth note (B-mi), whereas in the valid bass-solution, there is

an easily made ficta-mutation (of the 'implicit' and 'regular' kinds), involving the mutated

syllable ut and the mutant syllable fa (on the ficta-step B-fa-ut). With regard to the quoted

text, in a close comparison between Dowland's translation and Ornithoparchus's original, it

seems that "sharpe" is given for "vox mollis," and "flat" is given for "vox dura." However,

this is not the case, since Dowland's translation in other parts of the treatise give the

opposite equivalence between English and Latin. It would appear that Dowland's

original source). Clearly, Downland's edition has corrected the original, for such a placement in

Ornithoparchus's edition would find no reference in the text of that third rule. It seems also strange that the

mi-signs were intended for E and D in the part "Basis non valens," while its correction (in the part "Basis

valens") places the fa-signs on E and B. A minor discrepancy also occurs with reference to the signa

congruentiae, which are given in the original (though only in the tenor and the part labeled "Basis valens"),

but none are given in the translation.

176

terminology ("sharpe" and "flat") might also be applied and understood in the same way as

the modern concept of accidentals. Dowland's terms need to be understood only as an

anglicized references for the terms "durum" (or rather "vox dura," in this specific passage),

and "molle" (or "vox mollis," in this passage), and not as terms that share any relation with

the modern concept. Thus, despite the placement of Dowland's terms in the humanistic

environment of late-Renaissance England, the meaning of the medieval ficta-terminology is

still preserved, with no forecasting of the meaning (only of the name) each sign would

acquire in a much later future.

The indication of recta- and ficta-steps by ficta-signs may also be dependent on the

notational tendencies of the repertoire in each period, which may or may not be influenced

by specific theorists who proposed expansions of the recta-gamut (some including not only

seven hexachords, but nine or more hexachords—e.g., by including an -hexachord starting

on FF below Γ, or a -hexachord starting on cc, or even other hexachords both above and

below). For those theorists, steps such as B-fa, or FF-ut, or ff-fa would be considered

recta-steps. Otherwise, a ficta-sign can only imply a ficta-hexachord (and a ficta-mutation

where necessary) when it is placed on a step-station that has no correspondent mi or fa in

the recta-gamut—i.e., when the ficta-sign is clearly indicating a ficta-step.131 Below,

FIGS. 4 .6–4 .8 show illustrations of all these functions of ficta-signs, and the effects on

131 In FIG. 4 . 5 , this is the reason why the mi-signs placed on E and B (of the invalid

bass-solution) are indications of recta-steps, for E-mi and B-mi are step-designations duly found within the

recta-gamut. The opposite happens with the fa-signs on E and B (of the valid bass-solution), which must

be taken as indications of ficta-steps, for there is neither E-fa nor B-fa designations in the recta-gamut.

177

solmization created by changes in their position and their placement as indicators for ficta-

and/or recta-steps (and the hexachords within which they are found), as well as markers for

mutation.132

: ut re fa fa sol fa re ut ut

|

4 re=: =sol fa re ut re fa fa mi

|

4 fa sol fa sol mi

3 sol=

: =mi re sol fa la

3 sol fa mi re

FIGURE 4 . 6 - Functions of ficta-signs (ficta-mutation).

In FIG . 4 .6 , the fa-sign indicates both a ficta-step on E (where mi would be a

recta-syllable, but not fa), and the imminence of a place of mutation where the -hexachord

must replace the -hexachord. It may be reminded that all steps in a ficta-hexachord are

truly ficta-steps, whether or not they are unison to recta-steps. In the situation just

described, the designations C-re, D-mi, F-sol, and G-la are not found in the recta-gamut,

although they are virtually unisons to C-fa-ut, D-sol-re, F-fa-ut, and G-sol-re-ut. Since the

132 The words 'position' and 'placement' are used here as references to different aspects. The latter

refers to the ficta-sign in relation to specific step-letters (e.g., a sign may be placed on different loca: on E,

B, A, or any other step-letter); thus, it is called 'placement' with regard to the vertical alignment of signs on

the staff. The former refers to the ficta-sign in relation to notes (or note-shapes, where they can be

identified), independently from their loca; thus, it is called a 'position' with regard to the horizontal

alignment of signs on the staff.

178

ficta-sign is placed between the B and the D, it is fairly clear that the B should still be

solmized according to the -hexachord, while the D should pertain to the ficta

-hexachord. However, that D is a repeated note, and an 'explicit' ficta-mutation can be

easily implemented with the first D being solmized sol, and the second being solmized mi

(although it is an 'irregular' type of mutation, since there is a descending interval after that

D-mi). In FIG . 4 .7 , the fa-sign has been moved back to a position within the second

melodic gesture, between A and C (on the first staff).

: =ut re fa fa sol fa re ut ut|

3 re: =la sol mi re mi sol sol fa

|

3 sol la sol la fa

3 la=

: =mi re sol fa la

3

sol fa mi re

FIGURE 4 . 7 - Functions of ficta-signs (ficta-mutation).

That pre-positioning of the ficta-sign would appear to impose an early mutation

from a -hexachord (as shown in FIG . 4 .6) to a -hexachord, which could certainly be

made on the repeated C step (from a C-fa to C-re) that comes immediately after that sign.

Nevertheless, if that solmization is carried through, the -hexachord will become highly

uncharacteristic, not only because its solmization is limited to six notes that do not involve

its typical b-durum quality (by means of a B-mi), but mainly because after the pretended

179

mutation on C the step would be precisely a B-fa. This situation seems to suggest that the

second melodic gesture should in fact start with an -hexachord (not a -hexachord). At

the same time, if one takes into consideration statements that "we ought to avoid mutation,

and beware of them," or that "a mutation must not be made except for the sake of necessity,"

then the solmization of -hexachord must be carried through, up to a point where it can no

longer be maintained—that is, where one is about to find steps that will exceed the limits of

that hexachord.133 The location in question is found near the same place of mutation given

in the second of staff of FIG . 4 .6 (on the repeated D of the third phrase), accounting for an

'explicit' and 'irregular' ficta-mutation between D-la (of the -hexachord) and D-mi (of the

-hexachord). Thus, the function of a ficta-sign as a marker for the place of mutation (or

of its proximity) must be weighed against the effective necessity for enforcing that mutation,

against the aural perception of the eligible mutation-steps, as well as how the new

configuration of steps (the new hexachord) thereafter may affect the proper hexachordal

deduction of the previous melodic gesture (i.e., how it may affect the characterization and

solmization of the hexachord that precedes the sign). In order to make more conspicuous

the necessity for solmizing the -hexachord at the outset of (and throughout) the second

melodic gesture, the next musical illustration (FIG . 4 .8) will consider a different placement

for the ficta- sign: on B (but at the same position within the gesture as the sign placed for E

in FIG . 4 .7). Before starting the second phrase, the musician (who is already trained to read

133 The first statement is excerpted from Garlandia's Introductio musice (p. 1240; CS 1: 160):

"debemus mutationes evitare et eas percavere." The second statement is excerpted from Capuanus's

Compendium musicale (1415; La Fage 1864, 315): "non debet fieri mutatio nisi causa necessitatis."

180

ahead and anticipate changes) will clearly see the necessity for solmizing the -hexachord,

and later to mutate back to the -hexachord—thus assuring the solmization of the recta-step

E-mi (equivalent to modern e ) in the third phrase, since no other ficta-sign has been

notated.

: ut re fa fa sol fa re ut ut|

3 re=: =la sol mi re mi sol sol fa

|

3 sol la sol la fa

4 la=

: =re ut fa mi sol

4

fa mi re ut

FIGURE 4 . 8 - Functions of ficta-signs (ficta-mutation).

Notice however, that the -hexachord in question is a ficta-hexachord, for there is no

B-fa in the recta-gamut, nor is there a FF step-letter (whose solmization in this case would

be FF-ut). Both mutations in FIG . 4 .8 may then be classified as 'explicit' ficta-mutations,

though the first is 'regular' and the second 'irregular.'

Apart from enforcing hexachords in specific locations, the position of ficta-signs

may be naturally affected by the presence of ligatures. If a ficta-sign is applied to a step

within a ligature, the sign cannot be positioned immediately before that step, for it would

interfere with the ligature and prevent its appropriate reading—only in special conditions

may the ficta-sign be positioned close to a note within a ligature (e.g., close to the second

181

note of a podatus). There are at least two additional reasons for the deliberate positioning

of the ficta-sign away from the note it affects directly: the intention to enforce (or confirm) a

hexachordal reading different from than the one suggested by the melodic gesture; or

because a ficta-sign may be performing the function of a punctus divisionis (or divisio

modi). In fact, it is quite natural to suppose that if a ficta-sign is near to that of a punctus

divisionis (dot of division), the ficta-sign could be intentionally moved to the position of the

punctus, and visually perform that function of separation, while keeping its own function as

enforcer of a specific hexachordal reading. As in the case of the ligature, the proximity with

a ficta-sign could interfere with the appropriate reading of a punctus divisionis. In that

situation, it is possible that a scribe would choose to make the ficta-sign perform the

function of a punctus divisionis by momentarily occupying its position. Therefore, it must

not be overlooked that a ficta-sign could assume a mensural significance (even if

momentarily and in very special conditions), in addition to the functions previously

mentioned.134

134 Andrew Hughes seems to be the first who has clearly stated that a ficta-sign may function as a

punctus divisionis.

In mensural notation the grouping of notes and of notes and rests is often of primary importance.

The accidental [or rather, the ficta-sign] is placed early so that, for example, two minim rests and a

minim note will form a single group immediately obvious to the eye. There can be little doubt

that the necessities of mensural grouping cause some preplacements: many occur in prolatio major

or tempus perfectum where the grouping of perfections is specially important so that [mensural]

alteration and imperfection may be clear. In other words, the accidental sometimes functions as a

punctus divisionis.

(Hughes 1972, 61)

It must be noted that although a ficta-sign may serve as punctus divisionis, it may never serve the

182

Another matter to be addressed is the placement of a ficta-sign not on the line or in

the space, but either under or above the step to which it refers. This kind of occurrence is

likely to be attributed either to a later hand, or to occasional corrections the original scribe

may have made (due to some initial carelessness). In most cases, the melodic gesture will

be sufficient to solve any doubts about the step to which the ficta-sign is applied, or about

the additional functions the sign may perform, even if its position has been compromised by

a misplacement.135

The ability of medieval and Renaissance performers (or scholars) to read long

phrases ahead of time, generally used as a tool to solve problems regarding mensural

matters (alterations, perfections, etc.), was probably one of the most important factors in

solving problems regarding solmization and musica ficta. These might include: the

possibility of ficta-signs serving as punctus divisionis; the occasional misplacement of

sole function of a punctus perfectionis (dot of perfection)—the only possible exception is when the punctus

itself (if it were there) would be performing both functions at once.

135 Related to apparent mistakes, there is still another matter that may also be addressed: the

so-called post-positioning of ficta-signs, in which a given sign would be applied not only to the step that

may follow in that space or line, but also to steps that may precede. Andrew Hughes, for instance, has

explained what he calls a "retrospective effect," by relating this post-positioning of signs to the

post-positioning of tuplets and tuplet-numbers in romantic and modern music—e.g., the number is

frequently placed fractions of an inch (or even a few inches) after the actual beginning of the tuplet, usually

in the middle of the tuplet (whether or not it is marked by a bracket). Hughes also relates the

post-positioning of signs to the positioning of whole-measure rests, or whole-measure notes in the middle

of the measure, and argues that "[m]edieval performers were able to assimilate at a glance much longer

phrases than is possible with modern notation"—see (Hughes 1972, 69ff.). Anyone who has dedicated

some time transcribing medieval and Renaissance music will certainly agree with Hughes's statement, but

will not necessarily agree that it is the appropriate argument or proof of an intentional post-positioning of

signs. It seems more likely that a sign would not be deliberately post-positioned, unless by error and

unwanted omissions on the part of the scribe.

183

ficta-signs (although this possibility may not serve as justification for occasional errors or

omissions); problems regarding the deduction of hexachords by means of melodic gestures

and the presence of ficta-signs; or even decisions about the most appropriate place of

mutation in each given situation. These latter decisions, informed by the position of

ficta-signs (when they are present), are still a matter that deserves further consideration,

bearing in mind that although a mutation can be made either before or after the actual

ficta-sign, most of the time it is preferable to mutate before the sign, and certainly before the

step that is actually affected by the ficta-sign. Among Hermann Finck's set of nine "rules of

mutation," his seventh rule may serve to inform about this preference.

VII. Omnis mutatio fit tertia ante fa, si

adsit notula: si non, in secunda uel quarta

poterit mutatio inchoari.

(Finck 1556, bk. 1, f. F ir)

(7) Every mutation is made on the third

before fa, if the note may be present [in the

melody]; if not, the mutation may begin on

the second or fourth [before fa].

(my translation)

His statement allows for at least two different interpretations: one taking Finck's text

as a reference to 'syllables' before fa; another taking it as a reference to 'notes' (or,

'note-shapes') before fa. In the first interpretation, the words "tertia ante fa" appear to

denote the syllable re (i.e., "the third [syllable] before fa"), and "secunda uel quarta" the

syllables mi or ut (i.e., "the second or fourth [syllable before fa]"). In this interpretation,

Finck would appear to present an abridged version of the rule that 'mutation should be made

on places where the mutant-syllable can be solmized re, when it is followed by an ascending

motion, and la, when it is followed by a descending motion.'136 However, Finck already

136 This is the understanding given by Gaston Allaire—cf. (Allaire 1972, 52).

184

gives the unabridged version as his third rule, and there seems to be no reason (nor

intention) to provide an abridged version as a new rule that, in fact, creates an additional

confusion by taking the syllables mi and ut as possible mutant-syllables in lieu of re.137

Even if the seventh rule is interpreted as a further elaboration of the third rule, by

incorporating mi and ut as true alternatives for re, one would expect to find a similar

elaboration regarding alternatives for the mutant-syllable la. Finck provides no additional

elaboration, however. In the second interpretation, the solmization syllable "fa" is taken as a

reference to a "fa-sign," rendering the translation "the third [note] before the fa-sign" for

words "tertia ante fa," and the translation "the second or fourth [note before the fa-sign]"

for the words "secunda uel quarta." In this case, Finck's seventh rule is not understood as

a command about the most likely syllables to be used as mutant-syllables (as in his third

rule), but as a command about the position in which the mutation should occur (i.e., how to

determine what should be the place of mutation itself, or else, the step that should be taken

as a bearer for both the mutated and the mutant syllables)—regardless of the species, type

or case in which the mutation may be classified.138 In Finck's text, the absence of 'rule' that

137 The third rule has been quoted above, see p. 164.

138 In Finck's assertion, there is also the possibility of understanding "fa" as a reference to "a step

solmized with the syllable fa," which would render the translation "the third [note] before [the one solmized

with the syllable] fa" for the words "tertia ante fa," and the translation "the second or fourth [note before the

one solmized fa]" for the words "secunda uel quarta." This possibility would be same as the one that takes

"fa" as a reference to "fa-sign," but only if the sign is placed immediately close to the step that is supposed

to be solmized fa; in the case of pre-positioned signs (i.e., signs positioned two or more notes before the

one it may actually affect), this would be a different case. In any case, however, the seventh rule would also

be a statement regarding the 'position in which the mutation should occur,' and not with the 'syllables

(mutated and mutant) involved in mutation' (as it was the case with Finck's third rule).

185

makes reference to a mi-sign (i.e., a rule on how to choose the place of mutation in relation

to the position of a mi-sign) is not surprising, because fa-signs are used much more often

than mi-signs (either in polyphonic or monophonic contexts, and even in Finck's own time).

More to the point, the first book of Finck's treatise is dedicated to a presentation of the

elements of music in a plainchant context (which would hardly use any mi-signs).

In summarizing some of the main points discussed in this and in the previous

section, it may be stated that the place of mutation is the result of an equation that can be

solved only by observing three essential variables: the melodic gesture; the presence or

absence of a ficta-sign; and the position of the ficta-sign. The melodic gesture shows the

possible hexachordal spans, the ficta-sign enforces or confirms a specific hexachord over

that gesture, and the position hints to how soon or how late the actual enforcement (or

confirmation) of a hexachord is supposed to be effected. As mentioned above (fifth

guideline in section [iii], p. 148), although a ficta-step may serve as a marker for a

place of mutation (ficta- or recta-), which can be made either before or after the ficta-sign

(as demonstrated by means of the latter three musical illustrations), a mutation can never

occur on the step to which that sign is being applied. A change between hexachords, on the

precise step to which the ficta-sign is being applied, can occur only by means of

'permutation.'

186

— CHAPTER 5 —

PERMUTATION

In order to introduce the concept of 'permutation' there is probably no better

definition than the one given by Marchettus da Padova in his Lucidarium in arte musice

plane.

Permutatio est variatio nominis vocis seu

note in eodem spacio seu linea in diverso

sono.

(Marchettus 1317/18, tr. 8, ch. 1; Herlinger

1985, 270; GS 3: 89)

Permutation is a change in the name of a

syllable or note lying in the same space or

on the same line but with a different pitch.

(Herlinger 1985, 271)

Marchettus is considered the first theorist to have clearly enunciated the procedure, and also

the first one to have used (or chosen to use) the term "permutatio" in this particular context.

There is, however, debatable evidence as to whether or not 'permutation' (as defined above)

was systematically used in the repertoire that precedes the thirteenth or the fourteenth

centuries, or whether or not it was a vital (or even necessary) procedure. As a concept,

'permutation' can be apparently traced back to the mid- or late-ninth century, through a close

reading of some statements provided in the anonymous treatise Scolica enchiriadis

(abbreviated SE)—cf. (Anon. SE a.900, pt. 1; Schmid 1981, 61–62; cf. also Gerbert 1784,

1: 173–174; Migne 1844–84, 132: 983; [trans.] Erickson 1995, 34–35). For the purpose of

this discussion, Marchettus must be taken not only as the first theorist to have enunciated

187

'permutation,' but also the first one to have clearly conceptualized, defined and illustrated

such a procedure. The terms permutatio and mutatio are, in fact, virtually synonymous,

which perhaps makes Marchettus's choice seem somewhat misleading. However, it seems

to be exactly the close correspondence between those two terms that made his choice more

appealing, for both procedures can be understood in terms of their likeness, both

etymologically and with regard to the results associated with them, although they are

different with regard to process and necessity.139

Marchettus's treatises were transmitted into the Renaissance, and found in

Franchinus Gaffurius one of his most influential supporters, who also incorporated some

Marchettian ideas in his own writings.140 Nevertheless, Gaffurius seems to have displayed

some kind of resistance or criticism toward Marchettus, particularly with regard to

'permutation,' for whose practice and concept Gaffurius conceived some restrictions.141

139 Marchettus's choice also appears to be related to 'permutation' as a logical concept. Although

permutation, in this sense, is today understood under the mathematical processes that involve 'combinatorial

analysis' (which derives from nineteenth-century studies), it did already exist as a logical concept in the

late-medieval/Renaissance universe. At that time it meant simply the act of changing the order (or

arrangement) of elements within a given set of things (e.g., numbers, or even steps). Another meaning of

'permutation,' which is also likely to have driven Marchettus toward his choice, is the one regarding

rhetoric, for 'permutation' is the Latin equivalent for 'allegory' in Greek.

140 With respect to 'permutation,' Marchettus's most extensive explanations are provided in his

Lucidarium. One of the extant copies of that treatise is included in a manuscript entirely written in the hand

of Gaffurius—the manuscript in question (I-TRE) also includes Franco de Colonia's Ars cantus

mensurabilis, Marchettus's Pomerium, and the one-page anonymous Novem sunt species contrapuncti.

141 In his edition of Marchettus's Lucidarium, Jan Herlinger has stated that "Georgio Anselmi

(1434), Gaffurio (1492), and Lanfranco (1533) distinguished between mutation and permutation just as

Marchetto had, though Gaffurio warned against use of the latter" (Herlinger 1985, 13). Other theorists who

shared Marchettus's concept of permutation were: Bonaventura da Brescia, in his Brevis collectio artis

188

(The quotation below, from Gaffurius's Practica musice, will include two of the available

translations for the sake of comparison.)

In fa mi: quod ambae syllabae non sint eiusdem soni: nullam posse fieri mutationem plerique

consentiunt: maiore enim semitonio ab inuicem sunt disiunctae: [...]. Qua re: quum necessitate

coacti ipsam deducimus in fa mi mutationem et qualitatis et quantitatis conueniet mutatio:

qualitatis inquam idest proprietatis mollis in duram: mutando fa in mi: ascensus gratia: vel e

conuerso descendendi causa. quantitatis idest transeundo per fa ad mi ex grauiore ad acutiorem

sonum: ipsius apotomes interuallo: aut econuerso: per mi in fa descendendo ex acuto in grauiorem

quem quidem transitum quoniam difficilis et admodum dissonus est; omni solertia devitandum

musicorum scola precepit: hunc Marchetus et Anselmus permutationem vocant. Est enim ad

inuenta Irregularis et Indirrecta mutatio ad evitandum dissonum huiusmodi permutationis

transitum. quem vrgente notularum dispositione fieri necesse est.

(Gaffurius 1496, bk. 1, ch. 4, f. aviijv)

————————

The two syllables on fa mi do not sound

the same, and many think that no mutation

can take place, for the syllables are mutually

separated by a large semitone. [...].

Therefore, when necessity forces us to make

a mutation of both quality and quantity on

fa mi , a mutation of quality only, that is,

of soft proprietas into hard , will be made

by changing fa into mi because of an

ascending melody, or conversely, [of mi into

fa] because of a descending melody. A

mutation of quantity is made in going from

a lower to a higher sound by changing fa

Most authorities agree that on b fa and b mi

no mutation is possible since the syllables

do not both have the same pitch and since

they are a major semitone apart from one

another. [...]. When, therefore, we produce

that b fa-b mi mutation out of necessity, a

mutation both of quality and of quantity will

result. I speak (1) of quality, that is, of the

propriety of B-molle into B-durum by

changing fa into mi in order to ascend, or

conversely, in order to descend, and (2) of

quantity, that is, passing from a lower to a

higher sound by means of fa into mi at the

musicae [. . .] quae dicitur 'Venturina,' written in 1489 (esp. chs. 14 and 24; Seay 1980, 22–23, and 74);

Pietro Aaron, in his Libri tres de institutione harmonica, published in 1516 (esp. bk. 1, ch. 12, f. B viv);

Giovanni del Lago, in a Letter to Giovanni da Legge, dated 13 May 1523 (Blackburn 1991, 774–775,

[trans.] 781). Although Giovanni del Lago admits 'permutation' in his letter, he omits its possibility in his

treatise Breve introduttione di musica misurata (1540), perhaps because he thought it was not a suitable

procedure for beginners (the aim of his treatise), or else because he did not want to obscure his instructions

on mutation (and other aspects of solmization) with a procedure that was so complex to execute, and which

was not so essential. Similarly, da Brescia also did not mention 'permutation' in his Breviloquium

musicale (1497)—for translation see (Seay 1979).

189

into mi on the apotome, or conversely, in

descending from a high to lower sound by

changing mi into fa; this is a difficult and

very dissonant movement, and according to

musical scholars, it should be avoided with

all possible ingenuity. Marchettus and

Anselmus call it permutation. Irregular and

indirect mutation has been devised to avoid

the dissonant movement of such a

permutation, which must only be used when

it is absolutely necessary because of the

arrangement of the notes.

(Miller 1968, 39–40)

distance of this apotome, or conversely, mi

into fa, descending from a higher to a lower

pitch. Since this progression is difficult and

highly dissonant, the schools of music have

advised that it be avoided with every

ingenuity. Marchettus and Anselm call this

permutation. Irregular and indirect mutation

was conceived in order to avoid the dissonant

passage of such permutation, a passage

which must be made by an oppressive

arrangement of notes.

(Young 1969, 33–34)

Although the above quotation seems to start out with an assertive opposition to

'permutation,' it becomes clear (in the course of the statements) that Gaffurius was only

exercising the common humanistic mode of establishing theoretical and academic limits to

the concept (in the speculative sense), in order to impart some control over 'permutation' as a

solmization procedure (in the practical sense). In other words, Gaffurius was not against its

practice or concept, but sought a way to explain Marchettus's idea: (a) by narrowing its

dimensions (elaborating on instructions and parameters to its usage); and (b) by expanding

its scope (defining other possible situations not clearly described by Marchettus). Thus,

Marchettus and Gaffurius described a specific procedure by means of which one can

change (or rather, permutate) from mi into fa, or vice versa. No mutation (in whatever

species: recta or ficta) between those syllables was possible, and for some authors no

change (of any kind) could be conceivably made between them (whatever its name: mutation

or permutation). In terms of medieval and Renaissance descriptions, the main reason was

because both syllables (fa and mi) could not be found under one single step (defined as the

conjunction of letter-plus-syllables), at least with regard to the traditional recta-gamut. The

190

designation -fa / -mi, supposedly the only recta-place (together with its upper octave)

where those two syllables would be found, is actually the designation for a recta

double-step (a double-place) that represented two different hexachords (or different

qualities, following Gaffurius's explanation) and two different sounds (or different

quantities, according to Gaffurius). Even with regard to the ficta-gamut, although those two

syllables (fa and mi) could be found under the same step-letter, in most cases they would

produce a double-step yielding to two different sounds. Nevertheless, if the recta-gamut

and the imaginary ficta-gamut were merged, only a couple of steps would include all

possible syllables and still produce a unison under one and the same step-letter: D and G

(and their octaves). Naturally, a hexachordal change between the syllables mi and fa could

be called 'mutation' only when D or G (or their octaves) were eligible as places of mutation,

which seems sporadic at best, considering that in order to promote such an eligibility the

melodic transition between gestures would have to be greatly restricted.

TABLE II – Expanded gamut

t w e l v e - s t e p m e r g e d g a m u t

hexachords

: ut re mi fa sol la

: sol la ut re mi fa

: re mi fa sol la ut

: la ut re mi fa sol

: mi fa sol la ut re

: ut re mi fa sol la

: sol la ut re mi fa

191

The expanded gamut given in TABLE II (merging recta- and ficta-steps), shows all

the available syllables for each step-letter (only one octave is displayed with pitch-class-like

letters).142 The alleged rareness of a change happening exactly on D or G is due not only

to the frequency in which those steps might occur, and their unpredictable capacity to serve

as places of mutation, but is also due to the great distance (in terms of the circle of fifths)

between the hexachords involved in those specific changes. On a D, the mi-fa mutation

would have to occur only between an -hexachord and a -hexachords, and on a G,

between a -hexachord and an -hexachord. Otherwise, when other step-letters were

involved, a change between mi and fa would be necessarily called 'permutation'—a

procedure that was conceived precisely to allow and explain those changes that involved two

consecutive steps whose sounds were different (i.e., that did not meet in a unison).

In fact, permutation could be done in two distinctive cases: stepwise, and by leap.

The former case corresponds to the basic situation described and exemplified by

Marchettus (quotation above and FIG . 5 .1 below), and the latter case is deduced from

Gaffurius's statements and examples (quotation above and FIG . 5 .3 below)—numbers

referring to each note have been added to the modern transcriptions, for the sake of

clarifying the analyses of these musical illustrations. Stepwise permutation is very similar

142 It may be observed that when merging both gamuts, step-letters that are already fa cannot have

their sound modified (altered) when that syllable is solmized, even if a notated fa-sign ( ) is applied. Those

steps can have their sound modified only if a syllable mi is applied to them. Conversely, a step that already

includes the a recta-syllable mi can be appended with a syllable fa and perhaps have its sound modified, but

cannot have its sound modified by a mi-sign and the consequent solmization of the syllable mi . In other

words, syllables may not be duplicated under the same step-letter.

192

to 'explicit' mutation in that it involves two consecutive notes sharing the same step-letter,

although their individual sound is different. In modern terms this situation would

correspond to the chromatic inflection of a pitch—naturally, this procedure was not possible

in terms of mutation (which required two syllables on a unison). In this context, a

permutation would be indubitably marked by the presence of a ficta-sign applied to the

second note—e.g., from -fa to -mi (b to b ) or vice versa; or from c-fa to c-mi (c ' to

c ') or vice versa; or any other similar inflection, as shown in FIG . 5 .1 . Although

permutation by leap may be more common, stepwise permutation can be taken to represent

its most significant case, since it was the first to which the term 'permutation' was applied,

and the first to receive a clear definition, explanation and illustration (imparting authority to

Marchettus's presentation).

! !

! !

8

3 4 : mi fa/ : /mi fa

1 2 3 4

: la sol mi ut

4 3 fa mi/ : /fa mi

5 6 7 8

ut mi sol la

5 4 : fa mi/

: /fa

9 10 11

: re mi fa

4 5 fa/

: /mi fa

12 13 14

fa mi re

FIGURE 5 . 1 - Stepwise permutation. From Marchetto da Padova's Lucidarium

(1317/18, tr. 8, ch. 1)—cf. (Herlinger 1985, 272; GS 3: 89).

193

Before proceeding with the analysis of FIG . 5 .1 , some indications of mutation must

be revised, while others—devised to differentiate mutations from permutations—must be

explained. An 'explicit' mutation is indicated by means of an 'equals'-sign (=) placed after

the 'mutated' syllable, and another placed before the 'mutant' syllable. An 'implicit' mutation

is also indicated with both signs, except that the 'mutated' syllable is enclosed in square

brackets, in order to denote that such a syllable is only mentally intended (not uttered) by of

the performer. Paraphrasing the 'mutated/mutant' nomenclature, this dissertation will make

use of the term 'permutated' as a reference to the last syllable of the hexachord that is being

discontinued, and 'permutant' to the first syllable of the hexachord that is coming into effect.

In a permutation, the 'permutated' syllable is followed by slash, and the 'permutant' syllable

is preceded by a slash, in order to indicate that the permutation process involves a passage

from one syllable to the other in a place where the hexachords are disjunct. Notice that the

'permutated' and 'permutant' syllables must not be vertically aligned, since they are applied to

two different consecutive steps, and that an 'implicit' permutation cannot exist in any

circumstance.

In the transcription of Marchettus example for stepwise permutation (FIG . 5 .1),

double-barlines have been used to mark two distinct parts: one that starts with a permutation

from fa to mi, and is done within the limits of musica recta; and the other that starts with a

permutation from mi to fa, and involves the use of musica ficta. (In order to provide a clear

example, Marchettus carefully restricts any hexachordal changes to the upper voice, for the

solmization of the entire lower voice requires only syllables from the -hexachord.) In the

194

first part, the upper voice is marked by a fa-sign placed on b (seemingly in a signature-like

position), indicating that the first two steps must be solmized according to a recta

-hexachord, while step 3 is preceded by a mi-sign, indicating that the solmization should

proceed with syllables from a recta -hexachord—thus a recta-permutation is made from

-fa to -mi. The -hexachord solmization is interrupted by another fa-sign (on b)

positioned between steps 6 and 7—implementing another recta-permutation back from -mi

to -fa, and producing a return to the -hexachord solmization for remainder of the first part

(steps 7 and 8). In the second part of FIG . 5 .1 , although the mi-sign appears only near step

10 (indicating its solmization as c-mi, equivalent to modern c '), it is clear that steps 9 and

10 must be both solmized according to the ficta -hexachord.143 At the same time, the

fa-sign that appears on c, between steps 10 and 11 , enforces the solmization c-fa for that

latter step (a recta step, pertaining to the -hexachord, equivalent to modern c ')—a

ficta-permutation is then implemented from the ficta c-mi to the recta c-fa. Finally, the

solmization of the -hexachord is interrupted by the mi-sign on c, positioned between steps

12 and 13—implementing another ficta-permutation from the recta c-fa to the ficta c-mi,

and producing a return to the -hexachord for the remainder of steps in the upper voice

(steps 13 and 14).

In the stepwise case, however, 'permutation' may not always be restricted to a

hexachordal change between the syllables mi and fa, but may happen between any pair of

143 In case the entire example needed to be solmized without a break between its two parts, then

one would have to implement an 'implicit' mutation from the - to the -hexachord on step 9 —thus

mutating from d-la to d-fa.

195

syllables that, applied to the same step-letter, do not yield a unison—e.g., between C-ut and

C-mi, or C-sol and C-mi, or a-re and a-fa, or a-la and a-fa, etc.144

[Triplum]

(Pha)-ra-o-ne al -

: sol fa mire

[Motetus]

3

(fa)-cun - di –

: fa mire

[Tenor]

: sol

te-ro

mi fa[55]

mi

mi

fu-ga -

mi re

tur

ut/

mox

[mi=: =sol]

sol

:

lu

fa

3 fa

5

non

/mi

5

–

mi

mi

5

ut

mi fa

5

pi–

mi fa

FIGURE 5 . 2 - Stepwise permutation. "Garrit gallus—In nova fert—[Neuma]"

(mm. 54–60), from F-Pn fr. 146, f. 44v (Roman de Fauvel).

In all situations, there is a syllabic interval of third between the two consecutive notes on the

same step-letter, for which one of the steps must be solmized either as mi or as

fa—therefore must always be preceded by the correspondent ficta-sign indicating its

144 A few exceptions to this kind of change as 'permutation' are to be found in situations that can

be classified as simple 'mutations': from E-sol to E-mi (or their octaves), or from F-re to F-fa (or their

octaves), or else those changes between any syllable on the step-letters D or G (or their octaves); these

instances would all produce unison steps—cf. TABLE II.

196

solmization.145 A stepwise permutation from c-ut to c-mi (thus, from a -hexachord to an

-hexachord) is illustrated above (FIG . 5 .2), in the triplum (mm. 57–59) of Philippe de

Vitry's motet. In face of the intervening rest (m. 58) between the two permutation-steps, the

performer can, while pausing (though briefly), undertake a calmer aural conception of this

rather abrupt change of sound. Hence, it is an event that clearly represents one of the

smoothest ways in which this procedure can be performed, even though it is one of the most

difficult kinds of hexachordal change.146

A permutation by leap, on its turn, is defined as a procedure that involves two

consecutive notes represented by different step-letters—so that the difference with regard to

'quantitas' (following the nomenclature used by Gaffurius) applies to larger distinctions of

sound, and not only that of a semitone as in the stepwise case of permutation. The

permutation by leap commonly occurs when there is an intentional use of melodic tritones,

although other intervals may also happen.147 In general, a permutation by leap is solmized

145 Jacobus Leodiensis, in his Speculum musicae (p. 1330, bk. 6, ch. 66), classified the

hexachordal change that involves syllabic intervals of third among the first cases of what he called

irregularis mutatio—cf. (CS 2: 293; Bragard 1955–73, 6: 184–185).

146 The 'indirect' mutation that occurs in the motetus (m. 57)—already explained on p. —can also

be identified as a feature of solmization that parallels this kind of permutation, for they represent the easiest

forms of change of their kind.

147 Other leaps that necessarily call for a solmization by permutation would be augmented and

diminished intervals of octaves, sevenths, sixths, and fifths. However, not only these intervals are unlikely

to occur in the medieval repertoire or in most common exemplars from the Renaissance repertoire, but

some of them (such as augmented and diminished sevenths and sixths, or augmented fifths) were not

explained in historical treatises nor really conceivable in those epochs. There are still other leaps whose

solmization might be implemented either through 'permutation,' or according to the octave-equivalence

concept (depending on the hexachords involved), these are: sevenths (major and minor), sixths (major and

197

with the syllable mi for one step and the syllable fa for the other, although (as with stepwise

permutation) some cases may happen in which only one of those syllables is used for any

of the two consecutive notes involved in the procedure. Since that kind of permutation takes

either the syllable mi or the syllable fa for the solmization of any one of the notes, the

indication of a correspondent ficta-sign is customarily assumed, although they may not

always be explicitly present. When there are no ficta-signs, solmization of a tritone is

usually justified by harmonic needs, that is, in situations where harmonic consonances

might have priority over melodic consonances. However, permutations by leap may also

happen in pure melodic contexts, with no ficta-signs prescribing their solmization, so that

syllables must conform to the deductions made from observing the melodic gestures—a

musical example that followed Gaffurius's explanations on permutation (transcribed in

FIG . 5 .3 , below) illustrates these specific instances of permutation by leap, including some

circumstances in which mutations seem more appropriate.148

minor), and thirds (minor). In a few special instances of major sixths and minor thirds, a hexachordal

change may not even be necessary: in the case of major sixths, when the solmization calls for the use of the

syllables ut and la (e.g., from C-ut to a-la in the recta -hexachord, or from D-ut to -la in the ficta

-hexachord, etc.); in the case of minor thirds, either when the solmization calls for the use of the syllables

re and fa (e.g., from D-re to F-fa in the recta -hexachord, or from C-re to E-fa in the ficta -hexachord,

etc.), or when the solmization calls for the use of the syllables mi and sol (e.g., from E-mi to G -sol in the

recta -hexachord, or from F-mi to a-sol in the ficta -hexachord, etc.). These specific solmizations of

leaps of major sixths and minor thirds are not to be confused with the implementation of syllabic intervals

of third that characterizes 'stepwise permutation' (or 'irregularis mutatio,' in Leodiensis's nomenclature)—the

former situation refers to notes on distinct step-letters (with no mutations whatsoever), and the latter refers

to notes on the same step-letter (with clear hexachordal changes involved).

148 With regard to 'permutation' and 'mutation' (as well as other general references to solmization

and musica ficta), most medieval and Renaissance treatises seem to present a larger amount of melodic

illustrations and discussions, rather than harmonic ones. The exception of Marchettus's basic example

(FIG. 5 . 1 ) seems striking, for it shows a two-voice structure, even though his Lucidarium was dedicated to

198

!

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ 3

1 2 3 4 5

: ut mi re [ut=] : =sol fa

ÚÄÄÄÄÄ¿ÚÄÄÄÄÄÄÄÄ¿ 3

6 7 8 9 10

ut re ut fa/ : /mi

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ 3

11 12 13 14 15

re ut re [ut=] : =sol fa

ÚÄÄÄÄÄÄÄÄÄÄ¿

16 17 18 19

( :) ut mi ut re= : [=sol ]

ÚÄÄÄÄÄÄÄ¿ 3

ÚÄÄÄÄ¿

20 21 22 23

mi/: /fa ut re

3 ÚÄÄÄÄÄÄÄ¿

3

24 25 26 27

fa mi fa sol

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ 3

28 29 30 31 32

la fa/ : /mi re ut

FIGURE 5 . 3 - Permutation by leap (first solution). Transcribed from Franchinus

Gaffurius's Practica musice (1496, bk 1, ch. 4, f. a viijv).

plainchant, not polyphony. Moreover, there are also other two-voice examples in the Lucidarium, all of

them dealing with 'permutation' in some form or another—some of them including also the procedure called

'transmutation,' which will be later discussed in this dissertation. Marchettus's concept of 'permutation' was

deliberately linked with polyphony, probably because it was within polyphonic situations that he saw its

origin and necessity. In this respect, the status of Gaffurius's example (FIG. 5 . 3 ) seems as controversial as

that with Marchettus's. Even in a chapter "On musica ficta in counterpoint" ("De Fictae musicae

contrapuncto") where Gaffurius provides an illustration in a harmonic format and uses the term

'permutation' and related verbs, the presentation takes a rather melodic approach—cf. his Practica musice

(1496, bk. 3, ch. 13, esp. f. ee iijr) for the original text, and (Miller 1968, 146; Young 1969, 156–157) for

translations of the relevant passages. Also in bk. 3, ch. 2, esp. ff. cc viijr–v ("On the nature and

denomination [i.e., nomenclature] of contrapuntal species"—"De Natura et denominatione specierum

contrapuncti"), even though the main subject is not musica ficta, Gaffurius uses a similar melodic approach

(including conspicuous references to the of ficta and 'permutation') in order to discuss and define intervals

within a contrapuntal context—cf. (Miller 1968, 120–121; Young 1969, 126–127) for translations of the

relevant passages. It is evident, however, that links between musica ficta and polyphony are both

undeniable and inevitable, if not regarding the origin of musica ficta, at least because some specific

situations for the use of ficta can only be explained (or seem to arise) from a polyphonic standpoint.

199

Some of the statements in Gaffurius's treatise may shed some light on where the

permutations should be implemented, and where they should not.149 In the relevant passage

(repeated below, in order to provide a quick reference) Gaffurius clearly attests that

permutation is designed to be used only as a 'last resort,' and that, if necessary, 'irregular and

indirect' mutation should be used in its place.

[Quem] quidem transitum quoniam difficilis et admodum dissonus est; omni solertia devitandum

musicorum scola precepit: hunc Marchetus et Anselmus permutationem vocant. Est enim ad

inuenta Irregularis et Indirrecta mutatio ad evitandum dissonum huiusmodi permutationis

transitum. quem vrgente notularum dispositione fieri necesse est.

(Gaffurius 1496, bk. 1, ch. 4, f. aviijv)

——————

[T]his is a difficult and very dissonant

movement, and according to musical

scholars, it should be avoided with all

possible ingenuity. Marchettus and

Anselmus call it permutation. Irregular and

indirect mutation has been devised to avoid

the dissonant movement of such a

permutation, which must only be used when

it is absolutely necessary because of the

arrangement of the notes.

(Miller 1968, 40)

Since this progression is difficult and highly

dissonant, the schools of music have advised

that it be avoided with every ingenuity.

Marchettus and Anselm call this

permutation. Irregular and indirect mutation

was conceived in order to avoid the dissonant

passage of such permutation, a passage

which must be made by an oppressive

arrangement of notes.

(Young 1969, 34)

Following those precepts, together with an appropriate reading of the melodic

gestures, solmization should start with a -hexachord applied to first four steps, followed by

the solmization of an -hexachord at least up to step 9 .150 In this case, an 'implicit' mutation

149 The entire presentation concerning permutation has been quoted earlier on p. 189.

150 In fact, the entire gesture from step 1 to step 9 could have been read according to the

-hexachord if its compass was not exceeded by step 2 on e.

200

(c-ut to c-sol) from the - to the -hexachord should take place on step 4 , avoiding any need

for 'permutation' between steps 5 and 6 , whose leap must be interpreted not as a tritonus, but

as a diatessaron (equivalent to modern b and f , respectively). In face of these deductions

and the fairly consistent solmization of the -hexachord for most of the first ten notes, there

is virtually no way of avoiding a return to the -hexachord on step 10 , and a consequent

solmization of a tritonus between steps 9 and 10 .151 Thus a permutation must be

implemented in order to handle that tritonus, resulting in the 'permutated' -fa (on step 9),

and in the 'permutant' e-mi (on step 10). The next two hexachordal changes may only be

implemented as mutations: one needed near the place where the -hexachord is exceeded,

toward a gesture that denotes an -hexachord, thus imposing a mutation on step 14 (from

c-ut to c-sol); and the other needed as a return from that -hexachord to the former

-hexachord, thus imposing a mutation on step 19 (from c-re to csol).152 The return to that

initial -hexachord establishes itself as an ephemeral one, for the e (on step 20) is

immediately followed by a descending leap to b (on step 21), constituting an inevitable need

for a 'permutation' involving those two steps through the solmization of e-mi and -fa,

respectively. Further, step 21 establishes the beginning of a melodic gesture denoting a new

151 The only way of avoiding that tritonus would be by reading step 1 0 as e-fa (i.e., an e ').

This seems unlikely, not only because Gaffurius's intention is exactly that of illustrating the possible

alternations between avoidance of and compliance with permutation, but also because (in accordance with

that context) step 1 0 would have to be preceded by a fa-sign, in order to escape the -hexachord solmization.

152 The latter mutation on step 1 9 may be identified as an 'indirect' mutation (to which Gaffurius

referred as a possible alternative to permutation), since it involves an 'implicit' (non-uttered)

mutant-syllable—cf. the explanations on that sub-case of 'implicit' mutation at the end of section (iii), on

pp. 157–159.

201

(and last) return to the -hexachord (at least up to the c on step 27). The last gesture

(involving steps 27 and 28 to the end) is a matter for debate, probably even more than the

earlier ones. On the one hand, both -fa and e-mi constitute, by the end of the melody,

sounds well-ingrained in the mind of any performer that has complied with the proposed

solmization. In this case, the -hexachord could be retained up to step 29 (then solmized as

-fa), and a permutation would be implemented toward step 30 (then solmized as e-mi,

according to a -hexachord that would be valid for the remainder of the example)—this

latter possibility (shown in FIG . 5 .3) must be considered carefully, since it allows for an

almost symmetrical hexachordal solmization of the entire example.153 On the other hand,

Gaffurius has defended the avoidance of 'permutation' whenever possible, calling for an

interpretation of a leap of diatessaron from b (on step 29) to e (on step 30). In that case,

the -hexachord must be surely interrupted either on step 27 (c) or on step 28 (d), allowing

for a mutation to a -hexachord for the remainder of the melody, and establishing that b (on

step 29) as a -mi—this possibility is the one shown in FIG . 5 .4 , with the change that takes

on step 27 being classifiable as an 'irregular' mutation (from the 'mutated' sol to the 'mutant'

fa). However, a different hexachordal symmetry could be generated with the substitutive

solmization of the -hexachord on steps 19 to 21 (generating the sequence g-ut, e-la, -mi),

153 The hexachordal sequence would be = / = = / / —where 'equals' represents

mutation, and 'slash' represents permutation. This sequence establishes three groups separated by the two

permutations: the first (with the initial two hexachords) involving the first nine steps; the second (with

middle three hexachords) involving the next eleven steps; and the third (with the remainder two hexachords)

involving the last twelve steps—only in the latter group the hexachords are internally separated by a

permutation, while in the other groups the hexachords are conjoined by mutations.

202

where an 'irregular' mutation would be performed on step 19 (with re as its

'mutated'-syllable, and ut as its 'mutant'-syllable), and a permutation (formerly involving

steps 20 and 21) would be delayed to steps 21 and 22—this possibility is also shown in

FIG . 5 .4 .154 Notice that this latter possibility of permutation is not effected through the

syllables mi and fa, but uses a 'permutated'-syllable mi (on , step 21) and of a

'permutant'-syllable ut (on f, step 22).

!

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ 3

1 2 3 4 5

: ut mi re [ut=] : =sol fa

ÚÄÄÄÄÄ¿ÚÄÄÄÄÄÄÄÄ¿ 3

6 7 8 9 10

ut re ut fa/ : /mi

ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ 3

11 12 13 14 15

re ut re [ut=] : =sol fa

ÚÄÄÄÄÄÄÄÄÄÄ¿

16 17 18 19

( :) ut mi ut [re=] : =ut

ÚÄÄÄÄÄÄÄ¿ 4

ÚÄÄÄÄ¿

20 21 22 23

la mi/ : /ut re

3 ÚÄÄÄÄÄÄÄ¿

3

24 25 26 27

fa mi fa sol :

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ 4

28 29 30 31 32

[la=]=sol mi la sol fa

FIGURE 5 . 4 - Permutation by leap (alternative solution). From Franchinus

Gaffurius's Practica musice (1496, bk 1, ch. 4, f. a viijv).

154 In this case, the hexachordal sequence would be = / = = / = , showing a

symmetry in which the hexachords of each group are internally conjoined by mutations, and the

permutations reserved for separating the three groups: the first ( and ) involve nine steps; the second

( , , and ) involve twelve steps; and the third ( and ) involve eleven steps.

203

In both solmization-solutions given for Gaffurius's example (FIG . 5 .3 and FIG . 5 .4),

the recta-permutations are alternated with 'implicit' recta-mutations, but only FIG . 5 .3

presented the use of an 'indirect' mutation (on steps 19) as suggested by Gaffurius, while

the solutions in FIG . 5 .4 presented 'irregular' mutations (on steps 19 and 28)—the other

mutations were 'regular' (on steps 4 and 14), in both solutions.155

Whether permutations are made on stepwise motion or by leap, it is an extremely

difficult procedure to implement, since the performer must pass from one hexachord to

another without the support of a common unison, and there seems to be a scarcity of

theorists that would defend it as a justifiable procedure, at least if one looks for the use of

the term 'permutation' in association with that concept. Some authors have indeed used the

terms 'mutatio' and 'permutatio' as synonyms—e.g., Ramos de Pareja in his Musica

practica (1482, pt. 1, tr. 2, ch. 4, 31–34; [trans.] Miller 1993, 78–81); and Georg Rhau in

his Enchiridion (1517, ch. 1, f. B [viiijv]; ch. 2, f. C iv; ch. 3, ff. C iiijr–vr). Another theorist

who used these terms as synonyms was Heinrich Glarean, who is supposed to have known

very well the permutation-procedure associated with the Marchettian legacy. Nevertheless,

he withheld the knowledge of the procedure in his treatises, and even implied he was against

its practice, as it becomes clear in his Isagoge in musicen (1516, ch. 3; [trans.] Turrell

155 The solmization-solutions proposed by Irwin Young (relatively to Gaffurius's example) do not

seem appropriately interpreted from Gaffurius's statements, nor conform to the deductions of hexachords,

and other concepts presented in this dissertation—cf. (Young 1969, 34) for his transcription of Gaffurius's

example. In the specific case of the permutations, Young interprets that there should be a change between

-fa and -mi on every single b in the example. Permutations of this kind, as exposed above, can only be

made in a stepwise motion that requires two consecutive notes of the same step-letter (creating a chromatic

inflection)—an instance not found in any of the b instances given in Gaffurius's example.

204

1959, 119–122)—the quotation below (only the translation) is excerpted from that chapter,

entitled "Concerning the Permutation of the syllables," dedicated in fact to explain how

hexachordal 'mutation' worked.

[T]he distinction they [teachers of music] draw between "mutation" and "permutation"

impresses me very little, much less all the types of quality and quantity of mutation, and

I know not what portentious forms of proprieties and deductions.

(Turrell 1959, 121)

In fact, there seem to have been very few statements against 'permutation' in the

terms proposed by Marchettus, Gaffurius and others—Glarean's seems to be one of the

few, if not the only one to state such a conspicuous opposition. Most theorists did not even

discuss the existence of such a procedure, and some may have even avoided references to

it—either because they lacked a more appropriate or complete knowledge, or perhaps

because they did not find ways to oppose it in face of repertorial evidences. Even

Prosdocimus de Beldemandis (one of the foremost opposers of Marchettus's ideas) does

not seem to have spoken against the use of the term 'permutation' (or even mentioned it), nor

seems to have even implied any kind opposition to its practice. Prosdocimus's position in

this respect appears to be particularly curious, since he overtly stated his opposition to

Marchettus's divisions of the tone, and to the very signs Marchettus employed both as

indications of those divisions, and as indications for hexachordal changes. In a later

revision of his Parvus tractatulus de modo monacordum dividendi (A Little Treatise on the

205

Method of Dividing the Monochord), Prosdocimus writes about his intentions toward

Marchettian propositions.156

Omnia tamen ista diffusius et clarius

habentur demonstrative in tractatu quem de

hoc compilavi contra istos Marchetinos, qui

has erroneitates per Ytalian saltim

seminaverunt.

(Prosdocimus 1413-25/28, ch. 4; Herlinger

1987, 88)

All these things [about the divisions of the

tone] are presented more amply and more

clearly by demonstration in the treatise on

this matter that I compiled against the

disciples of Marchetus, who have

disseminated these errors throughout Italy.

(Herlinger 1987, 89)

(interpolation mine)

Despite the synonymical relation between the word 'mutatio' and 'permutatio,' the

concept and process that defines the latter term was also discussed by others, like the

anonymous author of the Berkeley Manuscript, although the term itself was not employed.

Quia ab una deduccione sepe sit

transitus ad aliam in cantu, quod absque

mutacione vocum bono modo fieri non

potest, licet aliquando fiat per disiunctas. Est

enim disiuncta vehemens transitus ab una

deduccione in aliam, absque quacumque

vocum mutacione ibi fieri possibile [...].

(Anon. Berkeley 1375, tr. 1, ch. 2;

Ellsworth 1984, 48, 50)

Although there may often be a

transition from one hexachord to another in

song (which cannot be accomplished in a

good manner without the mutation of

syllables), it may take place sometimes by

disjunctions. A disjunction is a violent

transition from one hexachord to another,

without whatever mutation of syllables

might be possible [...].

(Ellsworth 1984, 49)

(underlines mine)

In the above description, 'permutation' is implied by a reference to a process effected

"through disjunct" ("per disiunctas") syllables, performing a "violent transition"

156 According to Herlinger's commentary (1987, 11), Prosdocimus "seems to have undertaken the

revision of the Monacordum primarily to repudiate Marchettus's theories." The other treatise, to which

Prosdocimus refers in the quotation from the Parvus tractatulus ... monacordum, is his Tractatus musicae

speculative, written in 1425.

206

("vehemens transitus"). Similar statements that appear to descend from this Berkeley

lineage, are presented in Guerson's Utillissime musicales regule.157

Sequitur quartum capitulum

quod est de disiunctis

ET primo ponitur diffinitio secundum

Picttagoram

Disiuncta est vehemens transsitus soni

de vna proprietate: aut deductione in aliam

absque mutationis facultate vel sic

Disiunctio est progressio vnius vocis

vel deductionis ad aliam vbi esses neccessaria

mutatio tamen non fit [...]

Et dicitur disiuncta de disiungo

disiungis: quia vna proprietates vel deductio

disiungitur ab alia.

Et fit disiuncta vbi non debet nec potest

penitus causari mutatio.

Est tamen differentia inter disiunctam et

coniunctam: quia disiuncta disiungit:

Coniuncta vero coniungit duo extrema id est

duas voces diuersarum deductionum ad vnum

sonum vel tonum.

Disiuncta ergo dictitur et vocatur quando

disiungit vnam proprietatem ad alia

ascendendo vel descendendo pro vt inferius

sequitur et denotatur in practica.

(Guerson [ca. 1495], bk. 1, ch. 4, f. b iiiiv)

It follows the fourth chapter,

which is about the disiunctae

First, the definition is established

according to Pythaghoras.

A disiuncta is the drastic transition of

sound from one proprietas, or deductio [i.e.,

hexachord] into another without the

feasibility of mutation, or the like.

Disiunctio [i.e., disjunction] is the

progress of one syllable (vox) or deduction

toward another, where it might be necessary,

yet a mutation is not made [...].

And it is said disiuncta from [the verb]

'to separate' (disiungo, disungis): because

one proprietas or deductio is separated from

another.

And the disiuncta is made where a

mutation ought not or cannot be advocated.

Still, there is a difference between

disiuncta and coniuncta: because the

disiuncta separates; [and] to be sure, the

coniuncta unites two extremes, that is, two

syllables of different deductiones toward one

sound or tone.

Disiuncta, therefore, is said and is

named when it separates one proprietas in

consequence of another, by ascending or by

descending, inasmuch as it follows or is

specified in practice.

(my translation)

(ellipsis mine)

157 Other authors have made similar statements: Dionysius Lewis de Ryckel in De arti musicali

(15th cent., pt. 2, f. 116v); and Nicolaus Wollick in his Enchiridion musices (1512, bk. 2, f. c iiir).

207

Apparently, Guerson elaborated briefly on the statement from the Berkeley treatise

in order to provide a clearer understanding of the concept, even if no real expansion of

meaning was made.158 One or two generations after the Berkeley anonymous (and

approximately a century before Guerson), Petrus Tallanderius was still another author who

used the term 'disiuncta' in lieu of 'permutatio'—cf. his Lectura ordinata tam per cantu

mensurabili quam immensurabili. (ca. 1390, f. 162r–162v). In the quotation below,

although Tallanderius made no direct reference to 'vehemens transitus,' it appears that his

treatise would also pertain to the same Berkeley lineage, or perhaps to a branch derived from

that treatise.

Sequitur de disiunctione.

Nota quod disiuncta est ascensus vel

descensus sine mutatione et proprietate, et

habet fieri quando per mutationem non

possumus ad cantum attingere, et etiam quo

quomodo transcendat quintam.

(Tallanderius ca. 1390, f. 162r)

It follows [the chapter] on disiuncta.

Notice that disiuncta is an ascent or descent

without mutation and proprietas, and it has

to be done when through mutation we

cannot manage (administer) the chant, and

likewise when one may exceed (transcendat)

the fifth.

(my translation)

158 Although Guerson's statement seems to equate 'mutation' with 'coniuncta,' it becomes clear,

later in his treatise, that coniuncta may signify either musica ficta (or to ficta-hexachords) in the generic

sense, or ficta-mutation in the specific sense—cf. (Guerson [ca. 1495], bk. 1, ch. 4, f. b iiiiv; bk. 2, f. b

viir–viiir). These meanings for coniuncta were also used by a myriad of other authors, as well as by the

anonymous author the Berkeley treatise—cf. (Anon. Berkeley 1375, tr. 1, ch. 1, 2–4, 8; Ellsworth 1984,

44, 48–66, 86–88, 94–96 [even only]; [trans.] Ellsworth 1984, 45, 49–67, 87–88, 95–97 [odd only]). A

rather long list of other authors, who have used the term coniuncta (and also related words such as

coniunctio, coniungo, etc.), can be checked in the Lexicon musicum latinum, p. 628–643—all including

the meanings mentioned above, together with various others.

208

Ramos de Pareja also used disiuncta in the same context, although he judgmentally

qualified it as an 'improper' term—thus it seems that he would have preferred another term,

of which he apparently may have had no knowledge.159 Following previous authors,

Ramos de Pareja states that the term 'disiuncta' applied to changes from one proprietas to

another, without a mutation per se (i.e., without the use of a common-step).160 Thus, in his

definition of disiuncta (and through the case-descriptions he used), Ramos de Pareja clearly

equates that term with the basic concept of 'permutation': a procedure of hexachordal change

without the use of a common-step. At the same time, Ramos de Pareja gives no description

of a stepwise (chromatic) case similar to the one defined by Marchettus da Padova, but

expands on explanations about other features and applications of that basic concept of

159 It has been mentioned above that Ramos de Pareja did use the term 'permutatio,' although as a

synonym to 'mutatio,' in a chapter entitled "On the permutation of syllables" ("De vocum permutatione"),

cf. (Ramos de Pareja 1482, pt. 1, tr. 2, ch. 5, 25–27; Wolf 1901, 31–34; [trans.] Miller , 78–81). In a

detailed reading of that chapter, he seems to have applied 'mutatio' as the proper noun for the procedure, and

'permutatio' as a tentative description-noun of the procedure (in the sense of 'through mutation').

160 At the specific point from chapter 5 (pars 1, tractatus 2), quoted below, Ramos de Pareja's text

takes only the recta-gamut as basis for discussion; for this reason, he mentions only changes from one

proprietas to another (e.g., from a durum hexachord to a molle or a naturalis hexachord). In keeping up

with the context of Ramos de Pareja's chapter, however, the term disiuncta can also be applied to

hexachordal transitions without any change in proprietas—e.g., between two hexachords pertaining to the

durum proprietas (such as from a -hexachord to an -hexachord). Notice that Miller (1993, 86) translates

"property" for "proprietas," instead of the rendition "propriety" (preferred in this dissertation).

209

'permutation.'161 In the translation given below, the cases described by Ramos de Pareja

have been numbered individually, in order to facilitate the interpretations that will follow.162

[I]sti contemporanei nostri [...] disiunctas

improprie vocant, quando sine mutatione ab

una proprietate in aliam se transferunt, ut

puta: si reperiantur in c sol-fa-ut dicentes fa

et ad f fa-ut descendere immediate cogantur et

deinde ad graviores, tunc ille descensus

dicitur disiuncta, quia fa in altiori voce et fa

in inferiori pronuntiant. Sic et quando per

diapason saltus fit, ubicumque fit, semper

disiuncta fiet necessario. Dixi in diapason

necessario, quoniam in diapente non semper

fit de necessitate, sed solum, quando diapente

est mi mi ut e aut fa fa ut f k. Sed si

[cantus] fiat ab a la-mi-re existente cum re et

descendat per saltum diapente, immediate

illud re mutatur in la et dicitur re la re,

quoniam tunc bene sequitur illud re ab illo

la. Sic et in g existens cum ut saltu facto per

diapente immediata non fit disiuncta, sed

mutatur in sol et dicitur ut sol ut, quia bene

sequitur illud ut ab illo sol. Tritonus

immediatus semper causat disiunctas, ut si

ab f fiat saltus usque c sol-fa-ut transiens

unica notula, tunc dicitur in f fa et in

fa mi mi et sequitur c fa et tunc disiuncta

dicitur, quoniam illud mi non sequitur nec

[O]ur own contemporaries [...] improperly

call them disjunctions when they transfer

them without mutation from one property to

another; for example, [1] if they may be

found saying fa on c sol fa ut and must

descend immediately to f fa ut and thereupon

to lower tones, then this descent is called a

disjunction, because they may sing fa on the

higher tone and fa on the lower tone. And

so [2] when an octave leap occurs, wherever

it happens a disjunction necessarily will

always be formed. I said "necessarily in an

octave" because in a fifth it does not always

occur through necessity, but only [3] when

the fifth is mi mi, as e , or fa fa, as f k

[i.e., F to c]. But [4a] if it may be formed

from a la mi re by proceeding on re, and it

descends by a leap of a fifth, the re is

immediately changed into la and re la re is

said, for then that re is followed well by that

la. And similarly [4b] on g proceeding

with ut formed by a leap of a fifth, a direct

disjunction is not made, but ut is changed

into sol and ut sol ut is said, for that ut is

followed by that sol.

161 This lack of description and definition for the chromatic, stepwise permutation may also be

verified in the works of the authors pertaining to the Berkeley lineage, cited above.

162 According to Ramos de Pareja's nomenclature, the lowercase step-letters (a, b, c, d, e, f, g)

should be equated with the medieval uppercase step-letters (A, B, C, D, E, F, G), and the other step-letters

(h, i, , k, l, m, n, o, p) equated with the medieval lowercase step-letters (a, , , c, d, e, f, g, aa). Notice,

however, that when the author gives the full designation, the steps do follow the medieval

recta-nomenclature—e.g., c-sol-fa-ut, and a-la-mi-re. In the interpretive readings after the quotation, his

nomenclature will be converted to the appropriate medieval nomenclature adopted in this dissertation.

210

dependet ab illo fa graviori. Alii saltus, qui

maiores sunt diapente, semper faciunt

disiunctas tam in intendendo quam

remittendo, praeterquam ubi la possit accipi

in hexachordo, ut, si in a la-mi-re re aut mi

tenemus, cantus per saltum ad c fa-ut

remittatur; tunc la est accipiendum et dicitur

mi la ut aut re la ut. Aliter autem supra

diapente semper disiuncta fiet.

(Ramos de Pareja 1482, pt. 1, tr. 2, ch. 5,

29; Wolf 1901, 37–38)

A direct tritone always causes

disjunctions, as [5] when a leap is made

from f up to c sol fa ut by moving through

the single note ; then fa is said on f fa and

mi on mi [sic] and c fa follows, and so it

is called a disjunction because the mi does

not follow nor depend upon the lower fa.

[6] Other leaps greater than a fifth always

make disjunctions either in ascending or

descending, except [7] where la can be

applied in a hexachord, so that, if we use re

or mi on a la mi re a song may drop by leap

to c fa ut ; then la must be applied and

mi la ut or re la ut is said. But otherwise a

disjunction will always be formed beyond a

fifth leap.

(Miller 1993, 86–87)

(ellipsis, enumerations, and interjection mine)

Some of the musical descriptions used by Ramos de Pareja, however, represent

cases that do not constitute 'permutation,' but 'mutation' (which he uses as a logical converse,

in order to state what 'permutation' is not, and where it is not necessary). Below, the

interpretation of each case will present subtypes of 'permutation,' as well as those specific

possibilities in which it should not be applied, or even alternatives for avoiding that

procedure. Musical examples (not found in treatise) have also been prepared as illustrations

to the interpretive readings of each case, in compliance with Ramos de Pareja's

descriptions—in those examples, Ramos de Pareja's prescriptive solmization-syllables are

set in boldface.

The first description of disiuncta [1] involves a change between two melodic

gestures (separated by a leap of fifth): one ending on c-fa (thus solmized according to a

-hexachord), and the other starting on F-fa and descending to lower steps (thus

211

characterizing a solmization according to a -hexachord). Although that kind of change will

certainly configure a permutation (if Ramos de Pareja's prescriptive solmization is the only

one implemented), there are two other alternatives that do not create any permutation (if one

considers the existence of the other syllables in each step). The first alternative takes the

octave equivalence as an expediency to avoid permutation, by solmizing ut (based on the

-hexachord) as a mutant syllable for the step c-sol-fa-ut—this solmization would then

serve as an 'indirect' mutation (producing on that step the equation fa= [=ut], then

descending to F-fa-ut with the solmization fa (also based on the -hexachord).163 The

second alternative may use the -hexachord as a transient mediator between the - and

-hexachords wanted by Ramos de Pareja, implementing 'implicit' mutations on both steps

(c-sol-fa-ut and F-fa-ut). The step c-sol-fa-ut would take fa as a 'mutated'-syllable, and sol

as a 'mutant'-syllable (thus an 'irregular' mutation from the -hexachord to the

-hexachord); then the step F-fa-ut would take ut as a 'mutated'-syllable, and fa as a

'mutant'-syllable (thus a 'regular' mutation between the -hexachord and the -hexachord).

In FIG . 5 .5 , item (a) refers to Ramos de Pareja's original 'permutation,' item (b) refers to the

mutation obtained by means of the octave-equivalence expediency, and item (c) to the

mutations obtained by the mediation of the -hexachord.

163 In this first alternative, the 'indirect' mutation seems to be the better option, not only in

keeping with the prescriptive solmization given by Ramos de Pareja, but also because the solmization of

the -hexachord on c-sol-fa-ut would be obtained by means of an octave equivalence. However, it would be

also possible to implement a simpler 'implicit' mutation, in which the 'mutant'-syllable ut (according to the

-hexachord) would be the one uttered, and not the 'mutated'-syllable fa (according to the

-hexachord)—thus producing the equation [fa=] =ut.

212

!

!

!

(a)

: ut re fa mi fa/ : /fa re ut mi sol fa mi

(b)

: ut re fa mi fa=: [=ut]fa re ut mi sol fa mi

(c)

: ut re fa mi [fa=]: =sol [ut=] : =fa re ut mi sol fa mi

FIGURE 5 . 5 - Disiuncta ('permutation') by leap of fifth (fa / fa), and alternative

options of mutation—case [1] .

The second case [2] described by Ramos de Pareja, takes an octave leap as a sign

for 'permutation.' Although this is certainly one situation in which a hexachordal change

can only be implemented by means of permutation (since no hexachord reaches the octave

compass, and therefore there are no common steps in an octave leap), the octave-equivalent

solmization may be applied, if only to provide a momentary (mediator) 'mutant'-syllable for

the first step of the octave leap, or a momentary (mediator) 'mutated'-syllable for the second

step. In any case, a change involving an octave leap is certainly problematic (whether or not

it makes use of octave equivalence)—this is likely the reason why most theorists seem to

213

prefer 'irregular' mutation as a proper classification for this case (probably a much more

reasonable classification, for an octave correspondence between the two hexachords

involved can always be established). Since Ramos de Pareja provides no examples or

descriptions of steps involved in such a case, this could imply that an octave leap is easily

understandable by any reader, and that perhaps it is a common event.

The third case [3] asserts that in particular leaps of fifth one cannot possibly find

recta-hexachords that will share in any of the steps (thus, a 'permutation')—the author here

describes two cases. The first case is clear with respect to 'permutation,' for it refers to the

step-letters E and , since there exists no single recta-hexachord incorporating both in a

direct leap. At the same time, ficta-hexachords of the durum proprietas (e.g., -hexachord,

or -hexachord) do incorporate those two step-letters, and therefore may be used as

transient mediators for the solmization of the two distinct melodic recta gestures that

contain E and —see FIG . 5 .6 (a) for a representation of that description as 'permutation,'

and FIG . 5 .6 (b) for the mediated solution with a -hexachord (producing 'implicit'

ficta-mutations on both steps).164 The second case refers to the step-letters F and c, both

solmized fa (therefore F-fa within a -hexachord gesture, and c-fa within a -hexachord

gesture). This case does allow for a justifiable alternative through an -hexachord mediator,

since at least c-fa is already a step of that hexachord, and so is F when solmized with the

164 An 'indirect' mutation, like the one illustrated in FIG. 5 . 5 (b) , could also be presented as

solmization-solution for case [3] . This alternative would take E as a place of mutation, first solmized with

a 'mutated' uttered syllable mi , then aurally changed to a 'mutant' non-uttered syllable la (obtained by means

of octave equivalence)—generating the equation mi= [=la].

214

syllable ut. It also allows for another alternative through 'indirect' mutation, if the second

step of that leap is taken as place of mutation and solmized by means of octave equivalence

(thus generating a c-ut), and immediately proceeding to the -hexachord (whose

solmization, according to Ramos de Pareja's description, would still start on that

place of mutation with c-fa, since it forms a unison with c-ut), This latter case involving an

ascending leap from F-fa to c-fa (and its two alternative solmizations by mutation) is, in fact,

a restatement of case [1], described with a descending leap of fifth, and illustrated in

FIG . 5 .5 (together with two corresponding alternatives).

!

!

(a)

: ut mi fa re mi/ : /mi re ut fa mi re

(b)

: ut mi fa re [mi=]: =re [la=] : =mi re ut fa mi re

FIGURE 5 . 6 - Disiuncta ('permutation') by leap of fifth (mi / mi ), and an

alternative option with two ficta-mutations—case [3] .

The fourth case [4] is an attempt to narrow down particular leaps of fifth that do not

call for 'permutation' (i.e., disiuncta), but for 'regular' types of recta-mutation. This

alternative is justifiable when the step-letters of that fifth are found within the compass of a

215

single recta-hexachord. Ramos de Pareja presents two situations ([4a] and [4b]) in which

this alternative may happen. In situation [4a], he states that when a descending interval of

fifth is made from a-re (of the -hexachord) directly to d-re (of the -hexachord), then one

does not need to make a disiuncta, but could implement a 'regular' mutation on the

step-letter a (which is found both in the - and -hexachords)—thus producing a change

from a 'mutated' a-re to a 'mutant' a-la, and then proceeding with the leap to d-re. Similarly,

in situation [4b], when a leap is made from g-ut (of the -hexachord) directly to c-ut (of the

-hexachord), the hexachordal transition could be anticipated through a mutation on the

step-letter g (also found both in the - and -hexachords)—thus producing a change from

a 'mutated' g-ut to a 'mutant' g-sol, and only then proceeding to c-ut. In accordance with

those interpretations, situation [4a] is represented by the solmization sequence re la re, and

situation [4b] by the sequence ut sol ut. The two situations are illustrated in FIG . 5 .7 ,

respectively, in items (a) and (b).165 Although Ramos de Pareja described only

descending leaps of fifth in case [4], the solmization of ascending fifths could also use the

same kind of alternative mutations, provided the step-letters fall within the compass of a

single hexachord—in any event (ascending of descending) the first step of the leap would

be taken as a place of mutation. The same consideration of equivalence between descending

and ascending leaps of the same species (and quantitas) must be applied to the other

case-descriptions of the above quotation.

165 Notice also that Ramos de Pareja's justifications for case [4] may be used in favor of the first

alternative mutation proposed for case [1] , as illustrated in FIG. 5 . 5 (b) .

216

!

!

(a)

: ut re fa ut mi [re=]: =la re mi ut re fa la sol

(b)

: ut re fa ut mire [ut=] : =sol ut resol fa mi fa la sol

FIGURE 5 . 7 - Alternative mutations on a leap of fifth (re la re and

ut so l u t )—case [4] .

The description for the fifth case [5] starts with a gesture that involves a fifth, from

F-fa to c-fa, that interval is not reached directly, but mediated by a -mi, which therefore

establishes a leap of tritone with the lower step F-fa—see FIG . 5 .8 .166 Thus, it is truly

configured as a 'permutation,' for there exists no possibility of mutation (by mediation or

otherwise) in leaps of tritone, since that interval cannot be found in any conceivable

hexachord following the Guidonian paradigm. This case is even more characteristic of

'permutation' in that it involves the consecutive use of the syllables fa (for the

'permutated'-syllable) and mi (for the 'permutant'-syllable)—two syllables that cannot

usually yield to unisons.

166 In Miller's edition, the phrase "tunc dicitur in f fa et in fa mi mi" is translated with a slight

omission, a corrected version should read as follows: "then fa is said on f and mi on -fa / -mi."

217

!

: ut misol la sol 4 fa/: /mi fa re ut mi re ut FIGURE 5 . 8 - Disiuncta ('permutation') by leap of tritone (fa / mi )—case [5] .

The sixth case [6] is only a generic acknowledgment that leaps beyond the interval

of fifth are bound to be solmized by means of hexachords that do not find common-steps,

although the seventh case [7] discusses the exception of particular leaps of sixth.167

In case [7], Ramos de Pareja described two specific melodic situations of a

descending leap of sixth involving a-la-mi-re as the higher step, and C-fa-ut as the lower

step—which together outline the outer limits of a -hexachord, and may be solmized

respectively as a-la and C-ut. However, in the first situation (a), the higher step is also

prescribed with the solmization mi, implicitly determining an -hexachord solmization for

the gesture ending on that a-mi, whose solmization would then be changed to a-la, serving

as place of mutation between the preceding -hexachord and the subsequent

-hexachord—this situation is illustrated in FIG . 5 .9 (a). In the second situation (b), the

higher step is prescribed with the solmization re (thus, a-re), implicitly determining an

-hexachord solmization for the melodic gesture preceding that step, which would then

167 With regard to 'permutation,' the interval of sixth has been also discussed above in note 147,

and with regard to the exceptions of case [7] , it has been discussed in chapter 2 (iii).

218

serve as place of mutation between that -hexachord and the subsequent -hexachord—this

situation is illustrated in FIG . 5 .9 (b).168

!

!

(a)

3 : ut misol fa re [mi=]

: =la ut re fa mi fa sol mi re

(b)

: ut re fa 4 mi [re=]

: =la ut re fa mi fa sol mi re FIGURE 5 . 9 - Mutations on a leap of Guidonian sixth (mi la ut and

re la ut)—case [7] .

As the descriptions for case [7] exemplify, if the leap of sixth denotes the same

intervallic configuration of a Guidonian hexachord (T-T-S-T-T), then that leap may be

solmized according to a single hexachord and, therefore, will denote no hexachordal change

or any sort—neither a disiuncta (i.e., will need no 'permutation' to be solmized), nor any

'mutation.' A change will only be needed when the compass of that particular Guidonian

sixth is exceeded (above or below), and even then a 'mutation' will be the most likely

168 Notice that case [7] may serve as argument in favor of the mediated mutations proposed for

cases [1] and [3] , as illustrated in FIG. 5 . 5 (c) and FIG. 5 . 6 (b) , respectively.

219

procedure implemented. The reason for this latter interpretation is because a leap of this

magnitude would be normally followed by another smaller interval (either by leap or

stepwise) in the opposite direction—i.e., if it is an ascending leap of sixth, the next interval

would be descending; or if the sixth is descending, the next interval would be ascending.

Even on rare situations in which a melodic gesture proceeds above or below the extremes of

that leap of sixth, a simple 'mutation' will be usually possible, either taking one of the steps

that frame the sixth as a place of mutation, or taking the hexachord represented by that

Guidonian sixth as mediator.

In light of the above presentation, 'permutation' may be summarized as a procedure

of hexachordal transition implemented on two consecutive steps that do not meet on a

unison, whether it is done on chromatic, stepwise motions (following the concept exposed

by Marchettus da Padova), or on some particular leaps (following Ramos de Pareja,

Gaffurius, and others). Among these leaps, some intervals (however rare) may be taken as

definite signs for 'permutation,' such as: tritones, fifths (diminished), and octaves

(augmented and diminished).169 Some other leaps, like sevenths (major and minor), sixths

(major and minor), and thirds (minor), may denote the necessity for 'permutation'

(depending on the actual hexachords involved), but in other circumstances do not always

call for that rough procedure. Even if these latter intervals are mentioned as signs for

'permutation' ('disiuncta') in selected historical treatises, they must be judged first according

169 Cf. note 147, with regard to other leaps that could serve as signs for 'permutation,' but which

are not likely to be found in the medieval and Renaissance repertoires, as well as leaps that may or may not

call for 'permutation,' depending on the hexachords involved.

220

to their specific configuration (whether or not they fit within a Guidonian hexachordal

paradigm), and according to possibilities of applying other hexachords or alternative

concepts of solmization (e.g., use of ficta-hexachords as mediators, or use of

octave equivalence).170 In the specific case of fifths (perfect), there is usually an alternative

that enables a solmization according to one sole hexachord (even if only for that interval,

with mutations needed on its framing steps), provided one considers the use of a hybrid

gamut (recta plus ficta)—the mention of fifths as signs for 'permutation' ('disiuncta'), as in

the case of authors like Ramos de Pareja, is only applicable if solmization is restricted to the

recta-gamut.

170 Notice that the octave-equivalence concept has been formulated only for ephemeral situations,

when there are only a few steps outside that fall beyond the limits of only one hexachord, but which could

fall on a related octave-transposed hexachord. In situations when those steps create an individualized

melodic gesture, either a mutation, or a permutation is needed.

221

— CHAPTER 6 —

TRANSMUTATION

The term 'transmutation' refers to the momentary and punctual use of syllables from

an extraneous hexachord, while maintaining the solmization of a prevalent hexachord for the

surrounding notes (all within the same melodic gesture). In general, 'transmutation' involves

three consecutive steps: (i) a departure, 'transmutated'-step; (ii) a transient, 'transmutant'-step;

and (iii) a return, 'retransmutated'-step—although generally all three steps (or at least two)

may be aurally conceived according to the extraneous hexachord, its solmization (utterance)

is usually not applied to all. One of the characteristic examples of 'transmutation' happens

in the situation commonly know as fa-super-la—that is, when the sentence 'una nota super

la semper est canendum fa' can be applied. In this situation, the 'transmutated' and the

'retransmutated' steps are generally solmized according to the prevalent hexachord, and the

'transmutant'-step is the only one solmized with the extraneous syllable. Thus, the

'transmutant'-step constitutes a brief (transient) intervention that represents 'transmutation'

per se. Illustrated below (FIG . 6 .1), the fa-super-la situation is represented by a

'transmutant'-step -fa (on "cae-lorum"), preceded by a 'transmutated'-step a-la (on

"Regi-na"), and followed by a 'retransmutated'-step a-la (on the first note of "cae-lo-rum").

The illustration is an excerpt from one of the examples in Gallicus's Ritus canendi (1458/64,

222

pt. 2, bk. 2; Seay 1981b, 14: 59; CS 4: 380), which includes solmization-syllables for each

step (indicated in boldface in the transcription below)—the entire example (FIG . 6 .7) will be

discussed later in closer detail.

A – ve

: re fa mi re 3

ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

Re -gi - na cae -lo

ut fa sol la (fa) la

– – – – – rum

sol fa mi re ut re

FIGURE 6 . 1 - Transmutation in fa-super-la situation.

Here, the graphical indication of 'transmutation' has been devised as follows:

(a) the 'transmutant'-syllable is individually enclosed in parentheses, but no hexachord is

indicated—emphasizing its function as a transient intervention in the solmization of the

prevalent hexachord; (b) the 'transmutated' and the 'retransmutated' syllables are not

graphically differentiated from the other syllables of the prevalent hexachord (to which they

also pertain). Although Gallicus's original example gives only a single solmization-syllable

for each step, the syllables denote the hexachord applied to each note, and therefore, any

procedures of hexachordal change (transmutations or otherwise) are also made clear—even

though the places of those changes are not made explicit by means of the indicators devised

for this dissertation (equals, slashes, parentheses, brackets, etc.). The extensive melodic

gesture on the incipit of the antiphon "Ave Regina caelorum" ("Hail, Queen of the

Heavens") are clearly meant to be solmized according to a -hexachord, except for that

223

extraneous fa on the highest b-step, which would pertain to an -hexachord.171 However, it

may be noted that both the 'transmutated' and the 'retransmutated' steps may constitute

common-steps between the prevalent and the extraneous hexachord, and therefore may be

understood as potential places of mutation. If the mutation alternative is considered in

FIG . 6 .1 (even preserving Gallicus's prescriptive syllables), the first step a-la (preceding the

'transmutant'-step -fa) could be solmized according to the equation la= [=mi] (thus

producing an 'indirect' mutation); whereas the second a-la (following -fa) could be

solmized according to the equation [mi=] =la (thus producing a simple 'implicit' mutation).

What prevents this mutation approach is precisely the transient, momentary character of the

syllabic escape to an extraneous location beyond the upper limits of the prevalent

-hexachord—i.e., the escape to one sole note above la.

Another example of 'transmutation' happens when the solmization of a step must be

altered, for the sake of providing an appropriate interval in a cadential situation—that is, the

alteration of an interval that precedes a cadential arrival, for which one must observe the

prevailing tendencies of counterpoint in each time period (or even region, or composer, etc.).

This type of 'transmutation,' which implements subsemitone inflections, is usually based on

the contrapuntal precept of 'propinquity' (or 'closest approach'), whose basis Marchettus da

171 The notion of 'Heavens' is transmitted by means of a twofold word-painting on the first

syllable of "caelorum": (a) the highest step of the musical phrase is reserved for that place, representing the

highest place of the Heavens; and (b) the solmization syllable fa for that highest step pertains to the

extraneous -hexachordal realm (when observed from the prevalent -hexachordal realm), representing the

remote, almost unattainable Heavens (when observed from the earthly place of humankind).

224

Padova discussed in his Lucidarium, when talking about the "dissonances" of third, sixth,

and tenth.

9. Hee autem dissonantie et hiis similes

ideo compatiuntur ab auditu, quia sunt magis

propinque consonantiis, cum moventur

sursum et deorsum.

10. Oportet enim quod quando due voces

sunt in dissonantia que compatitur ab auditu

quod ipsarum quelibet requirens

consonantiam moveatur ita videlicet, ut si

una in sursum tendit, reliqua in deorsum,

semper distando per minorem distantiam a

consonantia ad quam tendunt.

(Marchettus 1317/18, tr. 5, ch. 2; Herlinger

1985, 202; GS 3: 80–81)

9. These dissonances, and those similar

to them, are compatible to the ear because

they lie closer to consonances as [their

notes] are taken upward and downward.

10. When two notes lie in a dissonance

compatible to the ear, each, seeking

consonance, must be moved so that if one

tends upward the other tends downward; and

they always must lie at the smallest distance

from the consonance toward which they tend.

(Herlinger 1985, 203)

A musical example illustrating this presentation, and clarifying what "the smallest

distance" is, comes only in a later chapter of that same part (treatise 5) of Marchettus's

work—chapter 6 entitled "Questio de dissonantiis" ("An Investigation Concerning

Dissonance").

FIGURE 6 . 2 - 'Propinquity.' (Marchettus da Padova

1317/1318, tr. 5, ch. 6; Herlinger 1985, 214;

cf. also GS 3: 82).

225

Marchettus's example shows alterations from minor to major on: (a) a sixth that

proceeds to an octave, (b) a tenth that proceeds to a twelfth, and (c) a third that proceeds to

a fifth. Although the basis of 'propinquity' is justified as a result of harmonic contexts, it is

the way of producing its inflections, in the melodic context of solmization, that needs to be

addressed. In the example, each segment of three harmonic intervals is clearly

individualized, bearing no relation with the others. Therefore, any solmization-solutions that

may arise for each voice of each segment must be taken as mere suggestions, since

hexachords and eventual transitions can only be determined by more complete melodic

gestures. It is in this sense that solmization syllables have been presented for each note in

FIG . 6 .3 (a transcription of Marchettus's example).

5

(a)

: ut (mi) ut

: sol la sol

5

(b)

: (re mi fa)

: la sol la

5

(c)

: ut/ : (/mi fa)

: sol mi re

FIGURE 6 . 3 - Transmutation in cadential situations ('propinquity'). From

(Marchettus 1317/18, tr. 5, ch. 6; Herlinger 1985, 215;

GS 3: 82).

226

In the case of the lower voice, a -hexachordal solmization can be coherently

applied to any of the three segments, but in the case of the upper voice, in which

hexachordal changes must be implemented, the solutions must be carefully considered. In

the upper voice, item (a) shows the only clear case that can be possibly solmized by means

of 'transmutation,' while item (b) shows no apparent need for a hexachordal change, and

item (c) shows a solmization by means of 'permutation,' since there is no possible

hexachord that could include both d-mi and a preceding d with a solmization that is clearly

other than mi. Item (a) illustrates the most characteristic case of a subsemitone inflection,

in which only the middle-step ('transmutant') is solmized according an extraneous

hexachord (c-mi of an -hexachord), while the surrounding steps are solmized according to

the prevalent hexachord (d-uts of the -hexachord). However, in subsemitone cases (as it

happens with the upper-semitone inflections of the fa-super-la situations) both the

'transmutated' and the 'retransmutated' steps could be solmized according to the extraneous

hexachord—in item (a) they could be solmized as d-fas of that -hexachord. If the

transient aspect that characterizes 'transmutation' is verified for all three steps, then they may

be all solmized according to that extraneous hexachord, without disfiguring the procedure of

'transmutation'; if only the middle-step is characteristically transient, then it will be the only

one solmized to the extraneous hexachord—but any of these decisions would definitely

need a more complete melodic gesture. In item (b), either all three steps may be solmized

according to the extraneous hexachord, or only the middle, 'transmutant'-step—the final

decision, as before, depends on a larger melodic context, within which the transient aspect

227

may or not be identified. However, the stepwise one-direction motion of that diatonic

contour suggests that no interruption should be implemented by that middle-step, and all

three notes should be solmized as a group. This latter consideration may paradoxically

allow that the first and third steps be taken as potential places of mutation (perhaps without

detriment to the transient aspect of the three-note gesture)—in this case, in order to indicate

the transitional character of the hexachord, it would still be advisable to keep all three steps

enclosed in parentheses, but as a group (as notated in FIG . 6 .3) and not individually as it

would happen in a more distinctive case of 'transmutation.' In a chromatic situation such as

the one shown in item (c), the proper identification of 'transmutation' (and of its transient

aspect) would also depend on a larger melodic context. In any case, a 'permutation' from the

first d to the second (prescribed by Marchettus as d-mi) is inescapable, and it remains to

decide whether the second step will be the only one taken as characteristically transient (in

which case it should be individually enclosed in parentheses), or whether both the second

and third steps will be taken as transients (in which case they may be enclosed in

parentheses as a group, as notated in FIG . 6 .3 , and not individually).

In FIG . 6 .4 , a more complete melodic context is shown, denoting a solmization

according to the -hexachord, within which three momentary departures occur: two as

fa-super-la situations (clearly upper-neighbor semitone inflections), and one as a cadential

situation (a subsemitone inflection). On the one hand, if a 'transmutation' is done in a

situation that finds an upper- or a subsemitone inflection, it will be generally adequate to

enclose in parentheses only the middle-step ('transmutant'), explicitly denoting its function

228

as a transient intervention (for the melodic gesture immediately returns to the prevalent

hexachord being solmized). If, on the other hand, there is a stepwise motion (either diatonic

or chromatic, as in Marchettus's example), it will seem more convenient to apply the

solmization of the extraneous hexachord either to all three steps, or to the two latter steps,

enclosing them in parentheses as a group (according to what seems fit for each case).

8

: re fa mi fa la

|

sol fa sol la

3 |

(fa) la sol la re

8

3 ( :) fa sol la (fa)

|

la sol fa mi

5 re (mi) re re

FIGURE 6 . 4 - Transmutation in fa-super-la situation (upper-semitone inflection)

and in cadential situation (subsemitone inflection)—melodic

context.

An illustration of the diatonic and chromatic cases can be seen in FIG . 6 .5 , although

there the transmutations are implemented in transitional (not cadential) situations, and the

context that supports the inflection is a melodic (not harmonic, nor contrapuntal). In an

exclusive melodic context such as the one illustrated below, the notation of the two mi-signs

will be mandatory if the inflections are intentional, for otherwise the performer would have

no idea where to implement these inflections.

229

8

: re fa mi fa la

|

sol fa sol la

3 |

(fa) la sol la re

8

( :) fa la sol (re 5 mi fa) mi re

|

fa mi re ut 5 (mifa) mi sol fa mi re

FIGURE 6 . 5 - Transmutation in fa-super-la situation (upper-semitone inflection)

and in transitional situation (diatonic and chromatic

inflections)—melodic context.

In face of the transitional situation (both in the diatonic and in the chromatic cases),

another solution for the 'transmutation' would be to solmize as extraneous steps only F-mi

and C-mi in the second staff—for that alternative solution, parentheses should enclose the

mi syllables individually, and the surrounding steps should maintain the -hexachordal

solmization. Thus the equation for those and for the surrounding steps would read as

follows: mi (mi) sol (on the diatonic E, F, G motion); and ut (mi) re (on the chromatic C, C,

D motion). At the same time, as it happened with Marchettus's example, alternative

procedures of hexachordal change may still be used in the solmization of FIG . 6 .5 . But

even assuming that these alternatives solmization are possible (with 'mutation' and

'permutation' in lieu of 'transmutation'), the extraneous hexachords (on and ) are

characteristically momentary occurrences with regard to the prevalent

-hexachord—FIG . 6 .6 will illustrated this situation below.

230

8

: re fa mi fa la

|

sol fa sol la

3 |

(fa) la sol la re

8

( :)fa la sol [mi=] : =re

5 mi fa=

: [=sol]mi re

|

fa mi re ut/ :

5

/mi fa [sol=] : =mi sol fa mi re

FIGURE 6 . 6 - Transmutation in fa-super-la situation (upper-semitone inflection)

with alternative Mutation and Permutation in the transitional

situations (diatonic and chromatic inflections)—melodic context.

In fact, in all situations (fa-super-la, cadential, or transitional), 'transmutation' may be

understood as a procedure akin to 'permutation,' as well as to 'mutation'—that is, a kind of

hybrid of the two former procedures. 'Transmutation' and 'permutation' are both

implemented in face of a brusque transition to a step that falls outside the realm of the

previous hexachord. The similarity with 'mutation' may be established with regard to the

'transmutated'- and 'retransmutated'-steps, which may sometimes serve as virtual

places of mutation. The major typification of 'transmutation,' and its consequent difference

with regard to those two former procedures, lies in that it is a momentary occurrence, or

transient intervention which may be due to sheer 'necessity' of avoiding unwanted

dissonances (causa necessitatis), or due to 'taste' of obtaining more 'pleasant' sonorities in

particular situations (causa pulchritudinis).

231

In order to understand the various instances of 'transmutation,' the sentence "una

nota super la semper est canendum fa" must be investigated first (both in its significance

and origin), for it is one of the most emblematic situations in which 'transmutation' may

happen. Nevertheless, no theorist (composer, scribe, or even performer) has yet been

identified as author of this sentence. One of the most conspicuous references to that

sentence is presented in Praetorius's Syntagma musicum (1619), though with a slightly

different wording.172

Es wisse doch ein jeder Cantor

vnnd Musicus vor sich selbstenwol/ daß/ wenn ein Tritonus oderSemidiapente vorfellt/ er einerechte Diatessaron, und Diapente, undbey der Clausula [f]ormali dasSemitonium singen und gebrauchenmüsse: Item unicâ notulâ ascendente

super la, semper canendum esse fa, &c.

(Praetorius 1619, 3: pt. 2, ch. 3, 31)

It is known, indeed, that when a tritone or a

semidiapente happens, every one singer and

musician [who] wants [to obtain] a proper

diatessaron or diapente before himself,

must begin and use the semitone at the

formal clause [i.e., the cadence]: thus, one

only note ascending above la must always be

sung fa, etc.

(my translation; cf. Lampl 1957, 80)

In Praetorius's treatise (and particularly in his Tomus tertius, zweite Theil—the part

to which the quotation above pertains), explanations for each topic usually employed

assertions in two languages: Latin and German. Following humanistic ideals, this method

of presentation was done in order to make use of a learned ambience and at the same time

172 In the original printed version of Praetorius's work, clauses in German were given in Fraktur

and clauses in Latin were given Roman typeface—in the quoted text, alternative typefaces have been applied

in order to represent those differences. The spellings have been maintained, with the exception of the

regular lowercase 's' that substitutes for its cursive lowercase version '∫' (without the lower curl); and the use

of an 'f' enclosed in brackets that substitutes for one instance of that same cursive '∫,' which had been

applied to the word "[f]ormali" in the original version. The correspondent translation for the Latin words is

set in italics, whereas that for the German words is set in plain text. According to Andrew Hughes (1972,

note 18), Praetorius's presentation should be "the earliest version" of that well-known sentence.

232

provide an easy path of understanding to the reader— the use of Latin phrases would then

impart authority to the text and serve as basis for discussion, while the German explications

(expanding and commenting on the Latin material) would provide the needed access to most

of Praetorius's audience. Thus, at a rhetorical level, those Latin assertions would be

functioning as 'commonplaces.' In the case of the quoted passage, there is only one

small-scale 'commonplace': the sentence "unicâ notulâ ascendente super la ...," whose

position at the end ascertains an implicit status both as basis for discussion, and as a

place of arrival for the previously made elaboration of the German commentaries. Taken

together, these factors characterize that sentence as a 'proverb': a short saying "popularly

known and repeated, usually expressing simply and concretely, though often metaphorically,

a thruth based on common sense or practical human experience."173 In terms of rhetoric, a

proverb ('proverbium') is considered neither prescriptive nor the only solution, but

(fulfilling the role of a small-scale 'commonplace') is regarded as a basis for further

elaboration of the subject under discussion, and an incentive to potential solutions, while

providing at least one. The notion of a 'proverb' is further corroborated by the presence of

the elliptical adverb "etc." (at the end of the commentary), suggesting that the reader should

be able to fill in any additional meanings, implied reasons or consequences that may come

from implementing that saying, and that no further explanation is explicitly required. In

other words, Praetorius was not providing any new statement, but a common, well-known

one (although he does not mention its origin). But in order to properly implement the

173 Cf. (Random House Webster's 1995, s.v. 'proverb').

233

solution presented by the proverb, one must observe if the restrictions of the situation to

which the proverb applies are satisfied. In fact, that Latin assertion is designed to present a

closing argument and a possible solution to one particular situation: the necessity to avoid a

tritonus or a semidiapente—it is only with regard to this situation (and its restrictive

intervals) that the adverb "semper" ("always") may be applied.174 In this context, the

sentence "una nota super la ..." must not be taken as a prescriptive 'rule,' whether in the

rhetorical or in the musical level of understanding. Also, the proverb makes use of an

'epitheton' (in fact, a customary resource used in 'commonplaces' and 'proverbs'), generally

defined as a figure of rhetoric that employs qualifiers (generally adjectives) to enhance the

perception of either the subject or the predicate of a sentence. In the case at hand, the

qualifier is also the solution itself: the determination of 'fa,' for it immediately suggests a

mollis (soft, suave) approach to a note that exceeds the upper limit of a hexachord, and even

serves as a further qualification for the restrictive factor of 'one sole note' (una nota/unica

notula)—that is, that 'one sole note' can only be 'fa.'175 In the musical sense (as well as in

174 The excessive implementation of the proverb fa-super-la, without the observing whether or

not there is need to avoid a tritone or diminished fifth, is the reason why Andrew Hughes declared that the

apocryphal sentence is an "unfortunate ditty" that "perpetuates the perversion of incorrect solmizing"

(Hughes 1972, note 18). Hughes, as well as Gaston Allaire (1972), discussed this 'proverb' by showing

that it was created rather as a way of avoiding the melodic tritone (if any was present), than as a postulate

that would be effected every time a melody reached a second above the hexachordal la. In his Musica Ficta,

Karol Berger (1987, 77–79) also discusses the 'proverb' and warns about its careless application and

perpetuation. Berger calls attention for the fact that it represents "merely one of the ways in which the

[melodic] prohibition of the tritone was formulated" (Berger 1987, 77).

175 Metaphorically speaking, the 'one sole note' (in face of the dissonant threat of the tritonus or

of the semidiapente) can only be implemented in a 'soft' manner, just as 'one sole person' who (in certain

specific situations of discord) can only interact with others by making use of a 'smooth' attitudes imposing

234

the rhetorical sense), that 'fa' will also serve as an ornament and emphasis to 'la' (as it is

proper of an adjective), thus generating an upper neighbor-note (an upper-semitone

inflection to 'la') that emphasizes the prevalent hexachord by a swift departure from and

return to its realm (as something/someone that leaves and longs for immediate, but smooth,

return).

Besides Praetorius's assertion, there is another, earlier and also conspicuous

statement of this proverb, provided by Hermann Finck in his Practica musica—the

quotation is drawn from his chapter dedicated to mutation, where it appears as the eighth

rule of mutation.

VIII. Propter unam notam ascendentem

supra la, non fit mutatio, sed semper fa in ea

est cantandum, nisi hoc , uel hoc

assignatum sit.

(Finck 1556, bk. 1, f. Fir)

8. A mutation is not made by reason of one

note ascending above la, but always fa in it

must be sung, unless this or this is

assigned.

(my translation)

Finck not only makes it clear (as did Praetorius) that the use fa must be

implemented only when there is one sole note that exceeds the limit of the prevalent

hexachord above la, but also presents two additional pieces of information: (a) such a

situation may not be called a 'mutation'; and (b) the situation will not happen if a mi-sign is

notated for the note above la. It may not be called a 'mutation' because that procedure

denotes a definite hexachordal change, something that does not happen with the transient

character of 'one sole, soft note above la.' The situation given in item (b) denotes that even

in dissonant situations (i.e., in the presence of a tritonus or semidiapente) the fa-super-la

a 'polite' ambience, 'someone' who is willing to work out compromises 'diplomatically.'

235

'proverb' cannot be followed if the dissonance is intentional. In this case, the intentionality

should be made clear by means of an explicitly notated mi-sign (in whatever shape)—an

occurrence which would probably impose a 'mutation,' or even a 'permutation.'

A near-contemporary of Hermann Finck, Maximillian Guillaud (in his Rudiments de

musique pratique) provides a similar (slightly earlier) statement with regard to the

fa-super-la situation, again with a different wording. Guillaud is perhaps even more

conspicuous in his instructions than Finck, for while he states that fa may not be

implemented in the presence of a mi-sign, he also assures that the syllable fa may be

implemented "even in the absence of" a fa-sign—at the same time, he clearly does not rule

out the possibility that the fa-sign may be duly notated.

Toustefois & quantes que par dessus ces six

voix s'en trouuera vne seule n'excedante que

d'une seconde, elle s'appellera fa, sans faire

muance, laquelle faudra profferer mollement

mesmement sans aucun signe de b mol,

pourueu que celuy de dur n'y soit mis.

(Guillaud 1554, tr. 1, ch. 5, f. A iiijr)

Whenever a note exceeds the six degree-

syllables by a second, this seventh note

must be called fa without making mutation

into the next hexachord. This note must be

sung flat (mollement) even in the absence of

any flat sign ( ) before or above it, unless

the natural sign ( ), were to affect it.

(Allaire 1972, 45)

Guillaud also brings in the 'soft' ('gentle,' almost 'languid') character to which the

epitheton expediency of the 'proverb' alludes.176

176 The mention of a sixth degree may seem to serve as a dismissal (in Guillaud's mid

sixteenth-century treatise) of any possibility of creating an additional solmization syllable for a seventh

degree. However, Allaire's personal translation should not be deceiving, for his "six degree-syllable" is

originally only and simply the "six syllable" ("six voix"), and the mention of a "seventh note" (which does

not appear in the original text) is only his attempt of provide a clearer (though misleading) translation.

236

It is clear, in light of these statements and of the explications given in the beginning

of this section, that 'fa' must not always be sung above 'la,' but only when a direct or indirect

tritone is unwanted. This reference to fa-super-la may be present even where the proverb is

not mentioned explicitly, but it would suffice to have the situation itself described: the

presence of unwanted tritone (direct or indirect). The earliest explicit description seems to

be found in the mid fifteenth-century treatise by Johannes Gallicus, although his assertions

appear to imply that this was not a new situation or procedure. In fact, by explaining its

occurrence in plainchant, and being himself a rather conservative theorist, he implies that

fa-super-la had been in effect for as long as plainchant tradition could be remembered.

[Discipulus:] Da mihi, quaeso, post haec de

plano cantu vel parvulum exemplum, ubi fa

prorsus de 3 rotundo propter tritonum

habeam, et quem non solum per litteras, sed

per illas syllabas et notas quadras modulari

queam.

Cantor: Exemplum quidem hic de plano

cantu tibi dabo clarissimum, quod modulari

te docebo per voces mixtas, hoc est, per

contrapunctum.

(Gallicus 1458/64, pt. 2, bk. 2;

Seay 1981b, 14: 59; CS 4: 380)

[Disciple:] Tell me, please, by means of a

plainchant or a brief example, where I may

in fact have fa out of the round b (b3)

because of the tritone, and how I may be

able to sing it not only through letters, but

also through those syllables and square

notes.

Cantor: Certainly, I shall give you this

most clarifying example out of plainchant,

for I shall teach you [how] it is to be sung

(modulari) through mixed voices, that is,

through counterpoint.

(my translation)

Despite the above reference to counterpoint, Gallicus illustrates this passage with a

monophonic example—the antiphon "Ave Regina caelorum" (transcribed below in

FIG . 6 .7), for which he presents a full solmization. A polyphonic example (a two-voice

version based on the same antiphon) was reserved by Gallicus for a presentation at the end

of the treatise (pt. 2, bk. 3; Seay 1981b, 14: 88; CS 4: 395)—the new, upper voice created

237

above the plainchant tenor is designated in this dissertation as 'contratenor.' In that

polyphonic example (transcribed below in FIG . 6 .8), the solmization for the tenor is

assumed from the previous, monophonic example, for only the contratenor is provided with

full solmization.177 In the two examples (monophonic and polyphonic), the presentation of

177 An excerpt of the monophonic example has been used earlier in this chapter (FIG. 6 . 1 ), in

order to illustrate the fa-super-la situation. An excerpt of the 'contratenor ' from the polyphonic example

has been used in chapter 2 (FIGS. 2 . 9 and 2 . 1 0 ), in order to illustrate the use of octave equivalence.

Gallicus's version of the plainchant does not correspond to two of the most common versions given in the

Liber usualis (LU, 274, 278), neither with respect to the words nor with respect to the music. However,

the version used as a chant at benediction in honor of the Blessed Virgin Mary (LU, 1864) does show partial

concordances to Gallicus's version—given below is a comparison between Gallicus's version—hereafter

(Ga), and the latter LU version—hereafter (LU).

Words: "Ave Regina caelorum, Mater Regis Angelorum, O Maria flos, virginum" — these

words are the same in (Ga) and (LU)

Music: on "A-ve" — (Ga) shows E-D-C; (LU) shows D-C

on "cae-lo-rum" — (Ga) shows a-G-F-E-D-C; (LU) shows a-G-F-G-F

on "cae-lo-rum" — (Ga) shows D; (LU) shows E-D

N.B.: There are no concordances (musical or textual) for the remainder of the chant: (Ga) has the

words "Ora pro nobis Dominum"; (LU) has the words "velut rosa lilium: funde

preces ad Dominum pro salute fidelium." Except that in (LU) there is melodic

gesture (D-E-F-E-D-C-D, mostly syllabic) on the "salu-te fidelium," which matches

with the gesture (mostly melismatic) on "Dominum," in one of the manuscripts of

(Ga)—see commentaries below.

There are also differences in the plainchant, between the two available editions of Gallicus's

treatise: Seay's edition (Seay), and Coussemaker's edition (CS). Seay used two manuscripts: as a primary

source he took GB-Lbm Harl. 6525 (apparently written on Gallicus's own hand or at least under his

supervision)—hereafter MS (H); and as a secondary source he took GB-Lbm Add. 22315 (apparently copied

by Nicolaus Burtius)—hereafter MS (A). Coussemaker, however, used only MS (H) for his edition.

Below, the differences between two manuscripts are listed as reported in (Seay); otherwise, if the manuscript

is not identified, differences are referred to the editions.

Words: (Seay) gives the spelling "caelorum," and "angelorum"; (CS) gives "coelorum," and

"angetorum" —otherwise they are the same

Music: on "an-ge-lo-rum" —(Seay) gives F-E (on "-ge-") and D-C (on "-lo-"); (CS) gives

F-E-D (on "-ge-") and C ("-lo-") (cont. ...)

238

solmization-syllables for each single step is significant in itself, for no earlier illustration of

full solmization appears to be extant. Since those solmization-syllables indicate the

hexachord that is being enforced at a given step (locus), the examples show not only which

hexachord is solmized for each melodic gesture, but also what procedures of hexachordal

change Gallicus's meant (as well as their cases, types, etc.), together with where the exact

place of change (locus) is in each situation—in Gallicus's examples only 'mutations,' and

'transmutations' are needed.

In FIG . 6 .7 , besides the fa-super-la 'transmutation,' whose 'transmutant'-step falls on

"cae-lorum" (already discussed above on pp. 222–224), there are two 'regular' mutations

(both involving the syllables re and la for the step-letter a): one on "Ma-ri-a" (an 'indirect'

mutation), and the other on "virgi-num O-ra" (an 'explicit' mutation). With respect to the

'transmutation,' it should be noted that (according to the quotation from Gallicus's treatise)

fa-super-la has been specifically used in the illustration for the sake of avoiding a tritone.

on "O-ra," set with the step-letters a-G — MS (A) gives the solmization la, ut; MS (H)

gives la, sol

on "Do-mi-num" — MS (A) gives E-F-E-D-C; MS (H) gives E-F-E-D; (CS) gives

the same as MS (H), except that the melisma D-E-F-E is applied to

"Do-mi-num," and two Ds are individually applied to the syllables "Do-mi-num"

Notation: (Seay), following mainly MS (A) in this example, gives solmization-syllables placed

at the left side of note-shapes (virgae and ligaturae based on the clivis pattern);

(CS), following MS (H), gives step-designations (letter-plus-syllable) placed on

the staff (in heightened-notation fashion) in lieu of note-shapes

Within the treatise itself, one minor melodic difference occurs between the monophonic example,

and the tenor used in the polyphonic example—on "Do-mi-num," the latter example gives the E-F-E-E (the

variants for the monophonic version are listed above). With regard to the polyphonic example, see also

note 64 (for a description of the notation), and note 180 (for other concordances and differences between the

two editions).

239

!

A – ve

: re fa mi re

3 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

Re -gi -na cae -lo

ut fa sol la (fa) la

– – – – – rum

sol fa mi re ut re

Ma-ter

ut re

ÚÄÄÄÄ¿ ÚÄÄÄÄ¿

Re -gis an - ge – lo – rum,

( :) fa sol mi fa mi re ut re 4

O Ma - ri - a, flos vir –

la sol la= : [=re] fa sol fa mi

(vir) – gi-num,

( :) re ut re= :

ÚÄÄÄÄ¿

O - ra pro no -bis Do -

=la sol la re ut re

ÚÄÄÄÄ¿

mi – – – – num.

mi fa mi re ut re

FIGURE 6 . 7 - "Ave Regina caelorum"—monophonic. From (Gallicus 1458/64,

pt. 2, bk. 2; Seay 1981b, 14: 59; CS 4: 380).

Solmization-syllables original to the treatise are set in boldface.

Gallicus was, in fact, referring to the indirect tritone that could have been created between the

b (on "cae-lorum")and two Fs, one on each side (the first on "Re-gina," and the other on

"cae-lo-rum")—both Fs being separated from the b by two notes (G and a). Thus, the b

must be solmized as -fa (even if there is no fa-sign prescribing its solmization), and the two

Fs must be solmized with the syllable fa (in compliance with the -hexachord denoted by

the melodic gesture). It must be noted that this is the only occurrence of a -fa, since there

240

are no other tritones to be avoided, and all of the other melodic gestures denote either the

continuation of the -hexachord or a sectional change to a -hexachord, on the verse "O

Maria flos virginum" (where the melody ascends to its highest steps, up to d-sol on "flos,"

and including the only -mi as the second step on "vir-ginum").178

With regard to the first 'mutation' on "Ma-ri-a," la (in boldface) is the only syllable

given for that step-letter a (re is not, and therefore is also not in boldface), but it is clear that

according to Gallicus's solmization this would be the only place to implement a mutation,

since it is clearly not done on the G-sol of "Ma-ria," and no 'mutation' would be possible on

the c-fa of "Mari-a." Thus, the only way to preserve Gallicus's prescriptive solmization is to

implement an 'indirect' mutation on that a-la-re, although it does not appear to have been the

best solution. It seems that a 'direct,' 'implicit' mutation would have been a more easily

implemented solution, with a non-uttered syllable la, and an uttered syllable re

(consequently represented by the equation [la=] =re). This solution would avoid an aurally

confusing situation that may arise from solmizing, immediately after that la, the syllable fa

with an ascending leap of minor third (semiditonus), since a previous ascending motion

from la to fa (for the 'transmutation' on "Regi-na cae-lorum") had already implemented a

semitone. The 'direct,' 'implicit' solution would then provide a clear leap of ditonus, whose

solmization within the restrictions of the Guidonian paradigm are only possible by means of

178 It is again significant to have a higher melody in this verse, since it is the first time that the

chant mentions the name "Maria," which is done by means of a vocative (thus calling directly onto Her

assistance), followed by the qualification of "flos virginum." Significantly, in the polyphonic example,

this is the section in which the 'contratenor' lowers itself below the plainchant melody—cf. FIG. 6 . 8 .

241

the pair re-fa, or the pair mi-sol.179 As for the 'explicit' mutation on a-la-re ("virgi-num

O-ra"), Gallicus's choice seems easily understandable, since it is indeed one of the most

easily implemented cases of mutation, requiring on the part of the performer no aural,

non-uttered conception of a sound or of syllable.

The polyphonic example will now be inspected with regard to the melodic gestures

and hexachordal changes in the 'contratenor.' In that example, the solmization-syllables

provided by Gallicus (only for the 'contratenor') are set in boldface in the transcription given

below (FIG . 6 .8). Other syllables are not set in boldface in the transcription, and include:

non-uttered syllables in 'implicit' mutations (according to the solmization prescribed by

Gallicus); syllables (either uttered or non-uttered) denoting alternative places of mutation;

179 Some additional considerations, with regard to the hexachordal passage that must happen

within the words "O Maria," may be made here, in order to speculate (and perhaps clarify) how the processes

of choice for a procedure and a place of change may have worked. It is highly unlikely in practice (though

theoretically conceivable) that Gallicus could have intended a 'permutation' from a-la do c-fa, since the aural

roughness for its implementation is generally the least preferred, and one of the cases (or subcases) of

'mutation' would be possible—a 'transmutation' is not an option here. Notwithstanding the above

mentioned solutions ('indirect' and 'direct' 'implicit' mutations), others (easier than 'permutation') would also

be conceivable, like performing mutations on the previous G-sol (on "Ma-ria"), or even on the previous a-la

(on "O Maria"). The latter possibility does not seem a good choice, since it comes right after a leap, and

there would be certainly a tendency to implement hexachordal changes after a stepwise motion (a much

easier situation to deal with aurally). The other solution on G-sol ("O Ma-ria"), even if facilitated by the

stepwise motion both before and after, would still be superseded by any solution on the second a-la-re ("O

Ma-ri-a"), which is aurally clearer, exactly because of the presence of that first a-la ("O Maria"), whose aural

conception is emphasized by the leap of fifth (provided it is solmized as la after re). Still another

possibility would be a mutation using a -hexachordal octave-equivalence on the c-fa ("Mari-a"), thus

imposing the solmization [ut=] =fa—which, however, would not be aurally preferable to Gallicus's 'indirect'

mutation, be because of an aural difficulty to implement an octave equivalence on the leap of ditonus,

especially given the expected solmization for that leap (as explained above).

242

[ ](Seay)

4

A – ve

: so l so l fa mi

: re fa mi re

[ ](CS)

4

Re-gi -na

fa re mi re

ut fa sol la

[ ]*

4

cae-lo – –

so l fa mi fa

³

3 (fa) la sol fa

[ ]*

– – –

fa so l la

mi re ut

rum

so l:

re

Ma-ter

[ut= ]=so l [re= ]

: =so l

³

ut re

4

[ ]*

Re -gis an - ge – lo

( :) re mi la so l la (fa)

( :) fa sol mi fa mi re

– rum, O Ma - ri - a,

la so l= [sol=]: [=re ] =re mi re ut

³

ut re la sol la= : [=re ] fa

flos vir –

fa [mi=]: =la so l

4 sol fa mi

4

(vir) – gi-num,

( :) fa mi re

( :) re ut re= :

4

O - ra pro no -

re mi re re

³

=la sol la re

bis Do -

la so l=: [=re ]

ut re

4

[ ]*

mi – – – num.

[ut=]=so l [la= ]

: =re mi fa so l

º

mi fa mi mi re

FIGURE 6 . 8 - "Ave Regina caelorum"—polyphonic. From (Gallicus 1458/64,

pt. 2, bk. 3; Seay 1981b, 14: 88; CS 4: 395).

243

and also the entire solmization for the plainchant 'tenor' (which is based on the solmization

for the monophonic example, and is given in FIG . 6 .8 for the sake of illustrating some cases

of mi-contra-fa conflicts and 'propinquity').180

The melodic outline of the 'contratenor' covers virtually the entire recta-gamut (from

A-re to ee-la). In the first verse ("Ave Regina caelorum") it covers exactly the compass of

the high region of the gamut (superacuta: aa-la-mi-re to ee-la), in second verse ("Mater

Regis angelorum") it moves to its middle region (acuta: a-la-mi-re to g-sol-re-ut), in the

third verse ("O Maria, flos virginum") it descends further to its lower region (gravis: A-re

to G-sol-re-ut), and finally in the last verse ("Ora pro nobis Dominum") it goes back up,

covering all three regions from Are to dd-sol. At least within each verse, the solmization

clearly follows the precepts and guidelines discussed in this dissertation. The transitions

between those regions of the gamut also follow the same precepts and guidelines, but due to

the intervallic leaps that must happen in order to make those transitions, the solmization

poses several aural difficulties to the performer. Thus, the performance of this 'contratenor'

180 (For the abbreviations used here, see note 177.) The 'barlines' that appear in FIG. 6 . 8 were

given only for the 'tenor' in (Seay)—the edition used for the transcription, and for both voices in

(CS)—since in that presentation they shared the same 9-line staff. The mi-signs in brackets ([ ] placed

above the upper staff), were given in the same way in Seay's edition (Seay), and without brackets in

Coussemaker's edition (CS). Those there are concordant signs in both editions were marked with an

asterisk in the transcription, the only discrepancy is marked with the abbreviation for the edition. With

regard to the fa-sign notated on "cae-lorum" (in the 'tenor' voice), it is given only in (Seay), and although it

is include in FIG. 6 . 8 , it is unnecessary for the solmization, as attested in the transcription of the

monophonic example in FIGS. 6 . 1 and 6 . 7 , and in the discussions related to them. (For additional variants

regarding the notation given in the two editions, see note 64.)

244

seems vocally problematic, and an instrumental performance could be more suitable.181

The first melodic gesture (on "Ave Regina caelorum") clearly denotes a

-hexachord, which includes a series of -mis (on "A-ve," on "Re-gi-na," and on

"cae-lo-rum") imposing false-relations with the -fa of the 'tenor' (on "cae-lorum"). Here

Gallicus is clearly unconcerned about those false-relations (which are observed in the

harmonic level), since it is far more important for him to avoid the tritone (observed in the

melodic level).

The second melodic gesture (on "Mater Regis angelorum") also denotes a

-hexachord (with its ut falling on G-sol-re-ut, whereas the ut of first -hexachord would

fall on g-sol-re-ut). In order to reach that middle region of the gamut, two consecutive leaps

are performed: a fifth from dd-sol to g-sol, followed by fourth from that g-sol to d-sol.

Thus the transition between the two -hexachords (represented in the steps dd-sol and

d-sol) is mediated by a -hexachord (represented in the step g-sol). For that solmization,

one must implement two consecutive 'implicit' mutations, by thinking (not uttering) the

'mutated'-syllable ut on g, and another 'mutated'-syllable re on d. There is no doubt that it is

a very difficult situation to perform and conceive aurally within the restrictions of the

181 As mentioned in note 65, the instrumental approach for the 'contratenor' seems probable,

mainly because of those two factors: the compass of the entire melody, and the transitional leaps.

Although there are also leaps within each verse, those are kept within the restriction of each region, and do

not exceed beyond the diatessaron—except, of course, on the last verse, which includes leaps of diapason,

diapente, and diatessaron, in order to cover all three regions of the gamut. In fact, this 'contratenor' appears

to be an exercise (or a demonstration) on how to compose melodies that are restricted to each region of the

gamut (in each of the first three verses), while producing transitions between those regions (by means of the

leaps), and resulting in an unfolding of the entire gamut (through the entire melody, and through the last

verse, which functions as a synthesis of the whole).

245

Guidonian paradigm. It seems conceivable, however, that this transition may be treated as a

'transmutation,' since the change to the -hexachord is momentary. In this way, dd-sol

would function as a 'transmutated'-step, g-sol as a 'transmutant'-step, and d-sol as the

'retransmutated'-step. But what prevents this solmization by 'transmutation' is that there is

no return to the same -hexachord; therefore, one would have to think of a 'transmutation'

with an additional, subsequent application of octave equivalence between the two

-hexachords. At the same time, if octave equivalence was used here (and if Gallicus

wanted such a resource to be applied), the g-step would have been better solmized as g-ut

(with no mutation), and the d-step would be constituted as the sole place of mutation

through the equation [sol=] =sol. Although this latter octave equivalence (without

'transmutation' and with one sole 'implicit' mutation) would appear to be the better solution,

Gallicus's solmization is trying to emphasize that the entire second verse must be thought of

on a different level, a different register, by changing the strata of the discourse, which

imposes a different hexachord (yet reminiscent of the first), that I will argue may find its

basis in a rhetorical procedure. Before the second verse and this second melodic gesture

come to an end, Gallicus prescribes one occurrence of 'transmutation' on "an-ge-lo-rum,"

precisely placed on the central note of the entire 'contratenor' melody. Although this

occurrence should be supported by the fa-super-la situation, there is no tritone to be

avoided, the only justification is the maintenance of the -hexachordal solmization with

which Gallicus wants to characterize the second verse, and thus must not be interrupted,

except if it is done momentarily. Also, there would be no sense in solmizing a larger

246

portion of melodic gesture with a different hexachord. Therefore, this transmutation may be

more clearly understood as an upper-semitone, or upper neighbor-note inflection, which are

also proper of 'transmutation' and may be understood as a 'generic' situation that

encompasses the more restrictive fa-super-la.

The third melodic gesture (on "O Maria, flos virginum") is also reached by means

of an 'implicit' mutation, in which both the last step of the second verse (d-sol, in the

-hexachord) and the first of third verse (D-re, in the -hexachord) can be used as

places of mutation. While uttering a 'mutated' sol on the d-step, one would be only thinking

of a 'mutant' re (according to the upcoming -hexachord, but an octave higher), thus

imposing an 'indirect,' 'implicit' mutation for that step. Conversely, on the D-step, one would

be thinking of a 'mutated' sol (according to the -hexachord, but one octave lower), while

uttering the 'mutant' sol (of the new -hexachord), thus imposing a 'direct,' 'implicit'

mutation. Thus, the consecutive occurrence of those two mutations establish a symmetry

(as can be seen in their graphical representation in FIG . 6 .8), which significantly

corresponds to a division of that antiphon in two halves (one for the first two verses, and the

other for the last two verses). The possibility of both mutations occurring consecutively,

creating those symmetries and the two inverted equations (sol= [=re] and [sol=] =re),

resembles a rhetorical figure called 'antimetabole,' whose definition is here given in the

words of Quintilian.

Fit etiam adsumpta illa figura qua verba

declinata repetuntur, quod antimetabole

dicitur: 'non ut edam vivo, sed ut vivam

Antithesis may also be produced by the

Figure called antimetabole in which words

are repeated with different inflections: "I do

247

edo.' [et] Quod apud Ciceronem conversum

ita est ut, cum mutationem casus habeat,

etiam similiter desinat: 'ut et sine invidia

culpa plectatur et sine culpa invidia ponatur.'

(Quintilian ca. 93/95, 9.3.85;

Russel 2001, 152)

not live to eat, but eat to live"; this is

adapted in Cicero in such a way that, though

it involves a change of case, the similarity

of terminations remains: "so that without

ill-feeling an offence is punished (plectatur),

and without an offence ill-feeling is laid

aside (ponatur).

(Russel 2001, 153; cf. Lanham 1996, 96,

s.v. 'Antimetabole')

In the same way, d-sol of the -hexachord is changed into D-sol, which may be

thought as a different inflection, since the difference in octave (as seen in chapter 2) is done

by changing a childlike voice into a adultlike one—the converse being done with d-re and

D-re according to the -hexachord. In fact, one may say that each of these occurrences (for

each hexachord), constitute individual 'antimetaboles,' and that the simultaneous occurrence

of both, together with the consecutive occurrence of the two 'implicit' mutations ('indirect'

and 'direct'), constitute a different, perhaps more complex example that creates a symmetrical

statement with the coupling of the two equations.182 Also significantly, the Latin word used

for the Greek 'antimetabole' is 'commutatio'—meaning 'interchange,' or 'changing

together'—which could be clearly related to the musical 'mutation' and understood as a two

'mutations' implemented together (close, consecutively to each other).

182 Some authors understand that a more complex, balanced, symmetrical figure of this kind

should be defined as 'chiasmus.' However, a 'chiasmus' is an inversion of ideas equated with 'antimetabole'

only when the inversion uses the same words, and differentiated when the inversion uses structures that are

equated but the words are different ('It is boring to sleep, to wake up is stimulating'), or else ('It is boring to

sleep, to eat is fulfilling'). In the latter example, though individually the ideas do not seem related, as in

the former, they are forced into such a relation by means of the grammatical structure: verbal-adjective plus

infinitive-verb, followed by infinitive-verb plus verbal-adjective—cf. (G. Burton 1999–2004, s.vv.

'Antimetabole' and 'Chiasmus') and (Lanham 1996, 96, s.v. 'Antimetabole'; 201–202, s.v. 'Chiasmus').

248

The second mutation in the third verse (also 'implicit') is implemented on

"vir-ginum," changing from the -hexachord (that occurred only for five steps) to another

-hexachord (the lowest). In fact, the presence of the F-step in the beginning of that third

melodic gesture is reason enough to impose the -hexachordal solmization on those first

five steps; otherwise, the -hexachord could have been solmized throughout the third verse.

One could consider that, as it happened in the previous verse, the F-step that falls outside the

-hexachord could have been solmized by means of 'transmutation.' However, that step is

preceded by a leap of fourth, and if it were to be solmized in that fashion (with a

solmization-syllable fa), it would have been preceded by a C also solmized with the syllable

fa (according to the -hexachord), which is not a usual solmization for such an intervallic

leap—the possibility of such a solmization (fa-fa) would traditionally be applied to leaps of

fifth.183

On the fourth verse (on "Ora pro nobis Dominum") the solmization and mutations

are graphically explained in the representations given in FIG . 6 .8 , which should be

understood in light of the presentation on octave equivalence, in which this passage was

used as illustration—see pp. 80–82.

With regard to the mi-signs enclosed in brackets [ ] above the solmization, as Seay

remarked (1981b, 14: 89n), they were distinctly included by "a later hand" in both

183 Cf. Ramos de Pareja's presentation on this subject, for which alternative solmizations of

'implicit' mutations were also conceived, as discussed above (pp. 214–215).

249

manuscripts he used for the edition of Gallicus's treatise. The table below will show how

they appear in Seay's and in Coussemaker's edition.184

TABLE III – Added mi-signs in Gallicus's two-voice Ave Regina caelorum (variants)

OCCURRENCE IN FIG. 6 . 8 STEP IN 'CONTRATENOR' STEP IN 'TENOR'

first—only in (Seay) cc-fa E-mi

second—only in (CS) cc-fa C-ut

third cc-fa a-la

fourth cc-fa E-mi

fifth f-fa D-re

sixth cc-fa E-mi

Apparently, if one observes only the first occurrence (given only by Seay), together

with the fourth and the sixth, it would appear that those mi-signs were provided in order to

avoid mi-contra-fa conflicts with the lower voice. However, mi-contra-fa is applied only

when the interval between the two voices is an octave, a fifth, or a fourth (or their

compounds). The only case with one of those intervals is the second occurrence (a

double-octave), but the 'tenor' is solmized C-ut, and therefore mi-contra-fa does not apply.

Moreover, if the solmization of the 'contratenor' is altered from cc-fa to cc-mi, it would

create an augmented double-octave, since that cc-mi would pertain to a ficta -hexachord

(thus making it equivalent to the modern c ", while the 'tenor' would be performing a

simple c). The other possibility for having those mi-signs is 'propinquity,' but which would

happen only when a third or sixth (or their compounds) moves toward a consonance of

184 Seay also presents the signs enclosed in brackets, whereas Coussemaker does not. Seay does

not mention variants between manuscripts, thus the table is given with references to the editions, which

may imply an editorial of publishing error.

250

octave or fifth (or their compounds). There are only two occurrences that fall on this

situation: the fourth and the sixth. In the fourth, however, the 'contratenor' is preceded by

another cc-fa which should also be altered in such a context, or a 'permutation' would have

to be imposed between those two steps—not only this would seem to contradict the melodic

gesture of the 'contratenor,' but also Gallicus (on account of this treatise) does not appear to

have ever defended, discussed, or acknowledged the possibility of 'permutation.' Therefore,

the only occurrence that seems to make any sense is the sixth, with the interval E-cc

(actually the penultimate interval of the that polyphonic setting) closing by contrary motion

on the double-octave D-dd. In any case, it must be noted that all those cases contradict the

original solmization prescribed by Gallicus, and are virtually unjustifiable—even if the last

one can be supported by harmonic precepts of 'propinquity.'

251

— CHAPTER 7 —

FIGURES OF SOLMIZATION AND FIGURES OF RHETORIC:THE MUSICAL DISCOURSE

The close relation that existed between rhetoric and music of the Middle Ages (as

well as Renaissance) has already been noted by several modern scholars, some dealing

directly with musica ficta, others with music in general.185 The links that exist between

solmization, counterpoint, and musica ficta are no less frequent, and must be addressed in

order to reveal (or at least attempt to unveil) one of the pieces of the hermeneutical puzzle

that can illuminate the understanding of historical practice and speculation, of notation and

theory.

As was mentioned above (note 139) in the presentation on 'permutation,'

Marchettus's choice for that term may have been influenced by its meaning in

rhetoric—'permutatio' being the Latin name for the Greek 'allegoria' (or 'allegory,' meaning

'to speak otherwise than it seems'). In its primary meaning, 'allegory' is frequently explained

as an extended (expanded) form of 'metaphor'—or, according to the definition provided by

Richard A. Lanham in his Handlist of Rhetorical Terms, an 'allegory' means:

185 For an example of authors who dealt with the relationship between rhetoric and musica ficta,

see (Atkinson 1990) and (Reckow 1992); for an example of authors who dealt rhetorica and music in general

see (Gallo 1963, 1975, 1981, 1985) and (Derksen 1982).

252

Extending a metaphor through an entire speech or passage; the rhetorical meaning is narrower than

the literary one, though congruent with it. The allegory is sometimes called “pure” when every

main term in the passage has a double significance, “mixed” when one or more terms do not.

(Lanham 1996, 41, s.v. 'Allegory')

Following the first phrase, it may be said that 'allegory' is a 'metaphor' (or series of

'metaphors') maintained throughout an entire phrase (or paragraph, or even an entire

discourse), instead of being restricted to only a few words. In order to understand better

what an 'allegory' is, and how it is differentiated from 'metaphor,' an example is given below,

excerpted from the first few verses of the triplum in the motet "Garrit Gallus—In nova

fert—[Neuma]."

Garrit Gallus flendo dolorose

Luget quippe Gallorum concio,

Que satrape traditur dolose,

Ex cubino sedens officio.

Atque vulpes, tamquam vispilio

in Belial vigens astucia

De leonis consensu proprio

Monarchisat, atat angaria.

The cock babbles, lamenting sorrowfully,

for the whole assembly of cocks mourns

because, while serving vigilantly,

it is trickily betrayed by the satrap.

And the fox, like a grave robber,

thriving with the astuteness of Belial,

rules as monarch with the consent

of the lion himself.

(Hoppin 1978b, 125)

This text can be stripped of its 'metaphors' or other figures, eliminating the 'allegory'

and producing a more direct, literal criticism against the desperate state of a society, the

corruption of its representatives, and the weakness of a monarch. In fact, even if some

isolated metaphors or other figures are maintained, 'allegory' will be decharacterized, for it

depends on the occurrence of various metaphors occurring (almost consecutively)

throughout the text, and not only in isolation. In the interpretive modifications produced

below, three figures will remain for further reference: one 'simile' ("... like a grave robber")

and two evident 'metaphors' ("the satrap," and "the lion himself").

253

The French barely speak and grieve painfully,

For the people of the entire French society suffer

Because while carefully observing their duties

They were betrayed by the satrape. ['metaphor']

And Enquerran de Marigny [the King's chief councillor], like a grave robber, ['simile']

Getting wealthier through corruption, wit, and evil-doing,

Rules as monarch, with the consent

Of the lion himself. ['metaphor']

In the case of the last 'metaphor,' the identification of the King with a Lion has at

least two meanings: one that is drawn from the word itself (the King is a Lion since he must

be a strong, all-powerful figure for all and everything under his kingdom); and another that

is drawn from the context (this is a weak, petty King, a ruler that is not true to its nature of

being strong and all-powerful, since he allows for corruption amongst his councillors, for

the suffering of his people, and finally grants excessive power to his chief councillor). The

second, contextual meaning applied to this metaphor, is also informed by the 'simile' (in

which the King's counsellor is explicitly and directly likened to 'a grave robber'), and by

another 'metaphor' of the King himself, through the word 'satrap' (a despotic, petty ruler). In

a certain sense, despite the attempt of decharacterizing 'allegory,' the fact that the context

implies new meanings is a sign that it has not been completely eliminated, especially

because the coherence of such a text depends on it (even if partially). Naturally, the same is

true of the procedure of hexachordal change called 'permutation,' for when the musical text

must be solmized using that procedure, its complete elimination may impair the coherence

of the whole (or at least of a particular passage). (In the ensuing discussion, the term

'permutation,' in its anglicized form, will be reserved as a reference to the musical procedure

of hexachordal change, and the term 'allegory' as a reference to the figure of rhetoric.) Note

254

that this idea of 'eliminating permutation from a musical text' does not refer to 'eliminating a

particular dissonant leap that must be solmized' (like a tritone), nor 'a chromatic gesture,' but

would mean 'trying to read, or go through, those situations without the aid of permutation.'

In some cases this 'elimination' can be done, and in other there is no way of avoiding

'permutation,' but even when it can be done, its elimination will certainly impose a change in

the understanding and coherence of a musical gesture.

Let me now return to Lanham's definition of 'allegory.' By saying that "the

rhetorical meaning is narrower than the literary," Lanham is in fact stating that although

every sentence is an allusion to something else (and therefore, has a double meaning), there

is only one, well-determined subject, that remains the same for the entire discourse (the one

that is being commented upon). Thus, the double meaning may be easily understood, for it

is limited (narrowed) to only two basic references: one consisting of the literal meaning of

the words used, and another of its meaning by analogy (relative to the subject about which

the commentary is being made). It is frequently possible to perceive that more than one

single commented-subject may exist for the same 'allegory,' but the interpretation will be

narrowed to one main subject, since it depends on the contextualization of all elements (even

when dealing with each possibility individually, and despite the wealth of imagery used in

the 'allegory'). Thus, in Lanham's assertion, the 'literary meanings' ('significants') are

broader and unbiased because of the wealth of imagery (wealth of 'signs'), and because there

may exist several possibilities of interpretation for individual (decontextualized)

elements—this is akin to the 'literal' interpretation in exegesis. At the same time, the

255

'rhetorical meanings' (or 'signifieds') are narrower because they exist only in a

contextualized situation, one that unavoidably keeps (in interpretation and audition) its

coherence to the commented-subject—this is akin to the 'allegorical' interpretation in

exegesis.186

In the same way, a musical 'permutation' has a broader (literal) and a narrower

(allegorical) meaning. The broader meaning is available through the individualities of both

the 'permutated'-step and the 'permutant'-step, which may have many meanings, since they

may pertain to several different hexachords at once. The narrower meaning is available

through the contextualization of those steps not only as part of a given melodic gesture, and

as part of particular hexachords, but also as parts of a process of change (whose meaning

differentiates them from the surrounding steps and from the steps used to implement other

kinds of hexachordal transition). As it happens with 'allegory,' in which the 'imagery' has no

apparent or immediate connection with the 'commented-subject,' so in music the two

consecutive steps that are going be the subject of 'permutation' have no apparent connection

with each other. The connection is established not only by means of the context, but mainly

by means of interpreting that context. In the musical case, this connection is established by

means of the need to solmize (read) the melodic gesture, and forge (interpret) a relation

between the two disjunct steps, by contextualizing their hexachords: 'permutation' is thus the

connection per se, turning individual 'imagery' into the 'permutant'-step, and the

'commented-subject' into the 'permutated'-step.

186 Cf. de Lubac 1959–63, esp. vol. 1 (translated into English in 1998, by Mark Sebanc).

256

Similarly, Lanham identifies two cases of 'allegory': "pure" (in which every element

in the discourse has a double meaning), and "mixed" (in which some elements do have

double meanings, while others do not). In a certain sense, these two cases may be made

analogous to (or may account for) the two main cases of 'permutation': the "pure" case

similar to 'stepwise permutation' (in which the double meaning of the step-letter is evident,

since it is a chromatic motion); the "mixed" case similar to 'permutation by leap' (in which

the double meaning is not readily evident, for it depends on the proper identification of the

situation, and whether or not there are alternative procedures of hexachordal change that can

be applied in lieu of 'permutation,' even though it might not be summarily ruled out).

In the case of 'mutation,' it may be related to the figure of rhetoric called 'metaphor.'

A basic definition of 'metaphor' (lit. 'transference,' or 'carrying beyond,' from the Greek

'metaphora') may be thus phrased: it is a procedure in which of a word (generally unrelated

to the subject at hand) is used in lieu of another word (related to that subject), the substitute

word being used to comment (either to enlighten, or to characterize, or even criticize) upon

the subject or one of its elements.187 Similarly, 'mutation' substitutes a syllable (from an

unrelated hexachord) for another (from the hexachord at hand in a given moment), no only

in order to allow solmization to proceed, but also stating that the new hexachord must be

acknowledged as part of the whole, and broadening the available context for interpretation

(just as a 'metaphor' informs about new possibilities of interpretation of a subject, and

187 In this definition, 'word' (in italics) is not a limited reference to one sole word (e.g., a noun,

verb, adjective, etc.), but may refer to more than one word (e.g., as in a noun- or verbal-locution), or even

to a phrase, or an idea—all of those, however, consisting of only one thing, or subject, or imagery.

257

broadens its perspectives).188 The speculations of Aristotle and of Quintilian (Marcus

Fabius Quintilianus) with regard to 'metaphor' may serve to enlighten these considerations.

We all naturally find it agreeable to get hold of new ideas easily: words express ideas, and therefore

those words are the most agreeable that enable us to get hold of new ideas. Now strange words

simply puzzle us; ordinary words convey only what we know already; it is from metaphor that we

can best get hold of something fresh.

(Aristotle Rhet., 3.10.1410b; Roberts 1924, 186)

————————

Incipiamus igitur ab eo qui cum

frequentissimus est tum longe pulcherrimus,

tralatione dico, que metaphora Graece

vocatur. Quae quidem cum ita est ab ipsa

nobis concessa natura ut indocti quoque ac

non sentientes ea frequenter utantur, tum ita

iucunda atque nitida ut in oratione quamlibet

clara proprio tamen lumine eluceat. Neque

enim vulgaris esse neque humilis nec

insuavis haec recte modo adscita potest.

Copiam quoque sermonis auget permutando

aut mutando quae non habet, quodque est

difficillimum, praestat ne ulli rei nomen

deesse videatur. Transfertur ergo nomen aut

verbum ex eo loco in quo proprium est in

eum in quo aut proprium deest aut tralatum

proprio melius est. Id facimus aut quia

necesse est aut quia significantius est aut, ut

dixi, quia decentius.

(Quintilian ca. 93/95, 8.6.4–6;

Russel 2001, 426, 428)

Let us begin then with the commonest and

far the most beautiful of Tropes, namely

translatio, which is called metaphora in

Greek. This is both a gift which Nature

herself confers on us, and which is therefore

used even by uneducated persons and

unconsciously, and at the same time so

attractive and elegant that it shines by its

own light however splendid its context. So

long as it is correctly employed, it cannot be

vulgar or mean or unpleasing. It also adds

to the resources of language, by exchanges

or borrowings to supply its deficiencies, and

(hardest task of all) it ensures that nothing

goes without a name. A noun or a verb,

then, is "transferred" from a place in which it

is "proper" to a place in which either there is

no "proper" word or the "transferred" term is

better than the "proper" one. We do this

either because it is necessary or because it

expresses the meaning better or (as I said)

because it is more decorative.

(Russel 2001, 427–429)

188 The comparison between 'mutation' and 'metaphor' is especially significant within the context

of musica ficta (i.e., especially when ficta-mutations are involved), for the new element it brings into the

interpretation of the whole is metaphorical in itself, since 'musica ficta' may be interpreted as a parallel

reality to the realm of 'musica recta.'

258

Thus, 'metaphor' is used in order to provide an appropriate meaning (and

understanding) to something that is not found among the regularly (commonly) known or

available array of things (ideas or words). 'Metaphor' is produced by analogy, i.e., by

changing an extraneous idea or word into something closer to common understanding, and

yet essentially different from that extraneous idea or word. Moreover, in 'metaphor,' this

analogy is not explicitly provided, i.e., the identification with that extraneous idea or word,

through something more regularly known, is simply implied, never directly addressed—as if

there was apparently no connection between the two. The connection is only established

within the context, and only after the analogy has been understood and ended. Thus is

irregular mutation, for it makes use of an already known position (within the hexachord

already being solmized), which is transformed into something that was originally extraneous

(the hexachord that will be solmized, ergo becoming known and common).

There exists, in fact, a close relation between 'metaphor' and 'simile,' which also

allows for some speculation whether 'mutation' is more akin to 'metaphor' or to 'simile.' In

this sense, the influential work by Quintilian (Institutio oratoria) may again provide an

insight; it explains more clearly the difference between the two.

In totum autem metaphora brevior est

similitudo, eoque distat quod illa comparatur

rei quam volumus exprimere, haec pro ipsa

re dicitur. Comparatio est cum dico fecisse

quid hominem 'ut leonem,' tralatio cum dico

de homine 'leo est'.

(Quintilian ca. 93/95, 8.6.8;

Russel 2001, 428)

In general terms, Metaphor is a shortened

form of Simile; the difference is that in

Simile something is compared with the

thing we wish to describe, while in

Metaphor one thing is substituted for the

other. It is comparison when I say that a

man acted "like a lion," a Metaphor when I

say of a man "he is a lion."

(Russel 2001, 429)

259

As seen above, in the sections dedicated to explaining 'mutation,' for pedagogical

reasons 'mutation' was described in historical treatises as a procedure that commonly

happened when two different syllables were applied to a single step, thus promoting the

change from one hexachord to another. In the graphical representation of 'mutation'

proposed in this dissertation, the 'mutated'-syllable is generally enclosed in brackets, and

followed by an 'equals'-sign, while the 'mutant'-syllable is simply preceded by an

'equals'-sign. By way of example, when the step-letter C serves as a 'place of mutation'

between a -hexachord moving to a -hexachord, the performer will arrive at that C as if it

was going to be solmized as ut (whose suggested representation would be [ut=]), but since

the change of hexachord is needed, a fa (whose representation would be =fa) will substitute

for that ut. If one assumes that 'simile' could apply in this case, that assumption may come

from the idea that a syllable is likened to the other via the 'equals'-sign (=). This is, however,

only a pedagogical representation, devised in order to provide an easy-to-understand

reduction. What really happens is that one syllable truly substitutes for the other, since the

hexachords have changed. In the situation described above, there is no way one could say

that 'c is like sol' at the 'place of mutation,' but that 'c is sol,' carrying with it and establishing

the context of a new, different environment: a different hexachord (as if another 'being,' or

another 'word'). There is, nevertheless, another possible interpretation that places both

'metaphor' and 'simile' under the umbrella of 'mutation'—or rather, as particular cases of

'mutation,' as it may become more evident, below, through an excerpt of the definitions given

by Lanham for each of these rhetorical figures.

260

Metaphor (G. "transference") — Translatio; Transport — Changing a word from its

literal meaning to one not properly applicable but analogous to it; assertion of identity rather than,

as with Simile , likeness.

[...]

Simile (L. "like") — Homoeosis; Similitude — One thing is likened to another,

dissimilar thing by the use of like, as, etc.; distinguished from Metaphor in that the comparison

is made explicit: “My love is like a red, red, rose.”

(Lanham 1991, 100, 140; 1996, 663, 949)

'Simile' is thus 'explicit,' while 'metaphor' is 'implicit.' Through these definitions,

'metaphor' can be simply related to 'implicit' mutation, in which one step suffers a change of

meaning by altering its individual solmization (the syllable, as the word) in a given moment,

imposing an analogy between its initial context and the context in which it will be

inserted—the whole process serving as a bridging between the two contexts: the two

hexachords. Elaborating further on the example that takes the step C-fa-ut as a

place of mutation (from the - to the -hexachord), if C-ut is assumed, the meaning of the

c-step will be drawn from the -hexachordal context, and if C-fa is used, then the meaning

will be established by the -hexachordal context. In this situation, neither C-fa is applicable

within the -hexachord, nor C-ut is applicable within the -hexachord, for individually they

have no meaning in those contexts. Their meaning, however, may change if the fact that

they share the same sound is used as analogy between them. It is this analogy that, in the

case of an 'implicit' mutation, asserts a new identity for that step: as place of mutation. An

identity revealed not only by the designation formed by the step-letter plus those two

particular solmization-syllables (C-fa-ut), but also by the equation [ut=] =fa, implemented

when it serves that particular role of place of mutation—which could be read: 'c is now fa in

lieu of ut.'

261

At the same time, 'simile' can be related to 'explicit' mutation, in which the

place of mutation is formed by two consecutive steps bearing the same step-letter, but which

are uttered with two different syllables (therefore two words that generate two different

individuals, two dissimilar identities). While their identity is distinguished from one another

by means of their distinct solmization utterance (as a practical and theoretical necessity),

their similitude is established by means of the common sound they produce (as an aural

manifestation), and also by means of the equation (as a graphical representation of 'explicit

mutation'). Still exemplifying by means of the same change between a - and a

-hexachord through C-fa-ut, there will be two distinct identities (C-ut and C-fa), where one

is likened to the other through the equation ut = fa—which could be read: 'c-ut is now read

as c-fa.'

Notice that although the result may appear to be the same, the conceptual process,

perception, and procedures for those two figures of rhetoric are different; just as the

conceptual process, perception, and procedures for the two cases of mutation are also

different, even if eventually their solmizational result is the same.

In fact, rhetoricians (both ancient and modern) consider 'metaphor' as one of the

most basic rhetorical figures; one that together with 'metonymy' serve as foundation for

almost all of the other figures (or at least for those called figures of substitution, and even

262

those that may be more precisely classified as figures of metaphorical substitution).189

Roman Jakobson has singled out metaphor and metonymy as the two main engines of

rhetorical language, passing down to modern critical thinking a basic distinction between metaphor

as indicating similarity and metonymy as revealing contiguity. [...]. Christine Brooke-Rose (in A

Grammar of Metaphor, [1958], pp. 23–24), after surveying all the definitions, settles on this plain

definition: "metaphor ... is any replacement of one word by another, or any identification of one

thing, concept or person with any other."

Perhaps it is metaphor’s intrinsic instability which has attracted so much recent attention: to

appreciate the metaphoricality of a metaphor we must posit a nonmetaphorical, normative "reality"

189 It may be noticed that 'color' is another term used to mean 'figures of rhetoric' in a 'generic'

sense—thus including both 'metaphor,' and 'metonymy,' as well as 'allegory' and 'simile.' However, 'color'

may also be considered in a more 'specific' sense as 'ornament,' frequently divided by rhetoricians into two

groups: the 'easy ornaments' ('ornatus facilis'), and the 'difficult ornaments' ('ornatus difficilis'). The figures

that may be listed within one or the other group usually vary between different auctoritates, although

generally speaking the both 'metaphor' and 'metonymy,' together with at least 'allegory' are listed within the

few basic ones under 'difficult ornaments.' For the sake of illustration, a list of figures within those

'difficult ornaments' is given below, based on the classification provided in the anonymous Rhetorica ad

Herennium (which includes only ten figures)—all figures are given alphabetically and with brief definitions,

except for 'allegory,' 'metaphor,' and 'metonymy,' discussed more thoroughly in the body of the text.

'Allegory ' -- See discussion above about 'allegory' and 'permutation.'

'Antonomasia ' -- This figure consists of a substitution of a proper name for an attribute that it

represents, or substitution of a periphrasis for a name, proper or common—e.g. "He proved a Judas

to the cause"; "You must pray to heaven's guardian for relief" (Burton 1999-2003, s.v.

'antonomasia,' access 11/18/03).

'Catachresis ' -- The use of a word in a context different from the original, due to the lack of a

more specific word to the current context—this figure is usually seen as a vice of rhetoric.

'Hyperbaton' -- Any inversion in the word order, i.e. in the normal syntax, or an insertion of a

word, usually for the sake of emphasis.

'Hyperbole ' -- The use of a word for the purpose of exaggerating some attribute or situation.

'Metaphor' -- See discussion above about 'metaphor' and 'mutation.'

'Metonymy ' -- See discussion below about 'metaphor,' 'metonymy,' and 'transmutation.'

'Onomatopoeia ' -- The use of a word, invented or not, whose sound imitates its meaning.

'Periphrasis ' -- This figure consists of a substitution of a descriptive word for a proper name, or

use of a proper name as a shorthand for attributes associated with it—usually it is seen as a kind or

specific case of 'antonomasia,' and may even be taken as synonymous to 'circumlocution' or to

Puttenham's 'ambage.'

'Synecdoche ' -- This figure performs a substitution of a part for the whole, or vice-versa.

263

against which to project the metaphorical transformation. The oscillation of the two reality states,

normative and transformative, provides the essential bounded instability of a bistable illusion.

(Lanham 1996, 664–665, s.v. 'Metaphor')

(interpolations and ellipsis in brackets mine)

As discussed above, 'mutation' (being akin to 'metaphor') also implements a

replacement of one syllable by another, changing the context and the identification of a basic

element—i.e., changing the hexachordal context and the individual designation of a step and

in a given moment (and sometimes changing also the conceptual proprietas). This change

of contextualized individuality is due, in fact, to the immutable, normative 'reality' of the

hexachordal paradigm—for it prescribes limits that must be exceeded for the sake of

providing broader contexts to the musical discourse, and therefore imposes changes

performed at selected passage-places (boundaries) between one hexachord and the other.

Also, the 'instability' (of which Lanham speaks) is intrinsically present in 'mutation' through

the ambiguity of its representative equation in the 'place of mutation.' It transforms and at

the same time imposes on one chosen step-letter a seemingly paradoxical duality: one side

of the syllabic equation indicating that the originating context is being discontinued, while

the other side indicates a new context that is yet barely established (sometimes even

hesitatingly, as when some 'indirect' mutation is being implemented). In 'mutation,' in fact,

the transformation of those individual contexts is established not only by the dual

hexachordal 'reality,' but also (as with any other procedure of hexachordal change) upon the

artificial 'reality' (which perhaps could be called 'fictional reality') of the paradigm itself.

What differentiates one procedure from another is established by the degree in which the

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comparison of context is understood and implemented. In 'mutation,' the comparison is

unequivocal (whether 'explicit' or 'implicit'), making its implementation immediately feasible.

In 'permutation,' as one step is not actually 'equated' with the other, the comparison between

the two contexts (hexachords) is not immediately perceived, and it takes a great deal of

effort to realize (i.e., both implement and understand) the connection between the two

contexts—just as in 'allegory' the 'imagery' or 'commentary' is perceived only after the a

complex connection is made with the 'commented-subject.' In 'transmutation,' however, the

comparison between contexts is marginal, that is, an auxiliary or subaltern context (whose

individuality is not even clearly stated) is eclipsed by a prevalent or dominant context, and

any change (as any actual comparison) is but ephemeral.

Having discussed the correlation between 'mutation' and 'metaphor,' and between

'permutation' and 'allegory,' the correlation between 'transmutation' and rhetorical figures

must also be investigated. Given that the Latin term transmutatio was used by some

rhetoricians as the equivalent to the Greek 'metonymy,' it seems conceivable to inspect if the

definitions and discussions about that figure of rhetoric will also apply the musical

'transmutation.' As used before in other sections of this dissertation, it seems appropriate

here to apply the rhetorical resource of substitution to the first few phrases of the above

quotation (from Lanham's work), using 'solmization' for 'rhetorical language,' and the

musical terms 'mutation' and 'transmutation' respectively for the rhetorical terms 'metaphor'

and 'metonymy.'

265

'Mutation' and 'transmutation' may be singled out as the two main engines of 'solmization,'

passing down to modern critical thinking a basic distinction between 'mutation' as indicating

similarity and 'transmutation' as revealing contiguity.

The 'similarity' that 'mutation' indicates (as does 'metaphor') is perceived when two

different syllables, each pertaining to a different hexachord, are applied (or applicable) to the

same step, constituting two elements on each side of the same equation. As mentioned

before, each of these elements (letter-plus-syllable) has an individual meaning within their

own contextual hexachord, but which are made equivalent (or similar) to each other by

means of their common sound (thus establishing their 'similarity' in the practical level). The

'contiguity' that 'transmutation' (as does 'metonymy') reveals is the one permitted by the

temporary, ephemeral enunciation of a syllable that does not pertain to the current

hexachord, and which does not implement a definite change to a new hexachord (conversely

to what happens in the cases of 'mutation' and 'permutation'), nor diverge from the context of

the current hexachord. Ergo, when 'transmutation' occurs, the 'transient' aspect of the

extraneous hexachord creates a sensation of a contiguity of the prevalent hexachord. This

hexachord is not being really interrupted, but ornamented, for its boundaries (la and ut) are

only momentarily crossed, without affecting the sense that the hexachord is still in force.

In 'mutation,' however, the similarity (obtained through sound, step-letter, and graphical

representation of the solmization) is made readily available and understandable, whereas in

'permutation' the dissimilarity is the first characteristic aspect, for the connection is obscured

by disjunct elements (steps) of individual hexachords that appear to share no

commonalities.

266

A more precise definition of 'metonymy' may help here in tracing its correspondence

with 'transmutation'—the quotation below is excerpted from the anonymous Rhetorica ad

Herennium, in which the anonymous author employed the Latin term 'denominatio' in lieu

of the Greek 'metonimia' (the definition itself is given in bolface, and examples are given in

plain text).190

Denominatio est quae ab rebuspropinquis et finitimis trahit

orationem qua possit intellegi resquae non suo vocabulo sit appellata.

Id aut a superiore re conficitur, ut si quis de

Tarpeio loquens eum Capitolinum nominet;

...; aut inventio, ut si quis pro Libero

vinum, pro Cerere frugem appellet; ...; aut

instrumento dominum, ut si quis Macedones

appellarit hoc modo: "Non tam cito sarisae

Graciae potitae sunt," aut idem Gallos

significans: "nec tam facile ex Italia materis

Transalpina depulsa est"; aut id quod fit ab

eo qui facit, ut si quis, cum bello velit

ostendere aliquid quempiam fecisse, dicat:

"Mars istuc te facere necessario coëgit"; aut

si quod facit ab eo quod fit, ut cum

desidiosam artem dicimus quia desidiosos

facit, et frigus pigrum quia pigros efficiat.

Ab eo quod continet id quod continetur hoc

modo denominabitur: "Armis Italia non

potest vinci nec Graecia disciplinis"—nam

hic, pro Graecis et Italis, quae continent

notata sunt; ab eo quod continetur id quod

continet, ut si quis aurum aut argentum aut

ebur nominet cum divitias velit nominare.

Harum omnium denominationum

Metonymy is the figure whichdraws from an object closely akin

or associated an expressionsuggesting the object meant, butnot called by its own name. This is

accomplished by substituting the name of

the greater thing for that of the lesser, as if

one speaking of the Tarpeian Rock should

term it "the Capitoline"; ...; or by

substituting the name of the thing invented

for that of the inventor, as if one should say

"wine" for "Liber," "wheat" for "Ceres";

"...;" or the instrument for the possessor, as

if one should refer to the Macedonians as

follows: "Not so quickly did the Lances get

possession of Greece," and likewise,

meaning the Gauls: "nor was the Transalpine

Pike so easily driven from Italy"; the cause

for the effect, as if a speaker, wishing to

show that some one has done something in

war, should say: "Mars forced you to do

that"; or effect for cause, as when we call an

art idle because it produces idleness in

people, or speak of numb cold because cold

produces numbness. Content will be

designated by means of container as follows:

"Italy cannot be vanquished in warfare nor

190 The ellipses, given by the editor/translator, indicate corruptions of the text, where there should

be explanations and examples, respectively: of inferior res for superior res; and of inventor for inventum.

267

magis in praecipiendo divisio quamin quaerendo difficilis inventio est,ideo quod plena consuetudo est non

modo poëtarum et oratorum sedetiam cotidiani sermonis huiusmodidenominationum.

(Anon. ad Herennium 4.32.43;

Caplan 1954, 334, 336)

Greece in studies"; for here instead of Greeks

and Italians the lands that comprise them are

designated. Container will be designated by

means of content: as if one wishing to give

a name to wealth should call it gold or silver

or ivory. It is harder to distinguish

all these metonymies in teachingthe principle than to find them

when searching for them, for theuse of metonymies of this kind isabundant not only amongst the

poets and orators but also ineveryday speech.

(Caplan 1954, 335, 337)

Thus, according to a particular ('generic') facet of the definition of 'metonymy,'

'transmutation' is that which uses a name of a smaller thing in lieu of another larger

structure, and although it may represent that larger structure, it also has an identity of its

own. This understanding of 'transmutation' also seems related to both 'synecdoche' and

'hypallage.' 'Synecdoche' is defined as a figure that substitutes the whole for its part, or

conversely the part for the whole—i.e., it implies the part by naming the whole, or it implies

the whole by naming its part. 'Hypallage,' as defined by Smyth is:

A change in the relation of words by which a word, instead of agreeing with the case it logically

qualifies, is made to agree grammatically with another case.

(Smyth 1956, 678; cf. Lanham 1996, 550, s.v. 'Hypallage')

The grammatical nature of this definition makes its relation to musical

'transmutation' especially significant. In 'transmutation' (as in 'hypallage') the syllable (or

word) of another hexachord (or case) is made to agree (grammatically) with the current

hexachord being solmized, even though it is clear that the syllable (either the fa in a

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fa-super-la situation, or the mi in a subsemitone inflection) is but a borrowing from another

hexachord with which it agrees by default.

Still another figure of rhetoric that may be inspected here is the one called

'metaplasm,' not only for being potentially equivalent to 'transmutation' as a procedure of

hexachordal transition, but also because it draws some relation to the other procedures and

to the historical definition of 'musica ficta' itself. The quotation below, presenting a

definition attributed to Henry Peacham seems here most appropriate for this inspection.

Metaplasm is a transformation of letters or syllables in single words, contrary to the common

fashion of writing or speaking, either for cause of necessity, or else to make the verse more fine.

(?Peacham 1593)191

This explication closely resembles those about musica ficta, in that 'metaplasm' (as

musica ficta) is defined as a change of the syllables of a single word (as the solmization

syllables of a single step), and further justified by cause of necessity ('causa necessitatis'),

or else by cause of obtaining a finer, more pleasant verse ('causa pulchritudinis'—i.e., by

cause of beauty). The "transformation" (mentioned in the quotation) may be exemplified by

the word 'theatre,' which suffers an alteration into 'theater'—an example that is actually a

specific type of 'metaplasm,' more properly called a 'metathesis.' 'Metaplasm' is more

properly a phonetical transformation (or alteration) done by means of augmentation,

suppression, substitution, or only transposition—in the case just exemplified above, it is a

191 Lanham's work (1996, p. 666, s.v. 'Metaplasm') is the source of the attribution to Peacham,

and from which the quotation was drawn. However, the quotation could not be located in Peacham's The

Garden of Eloquence (either in the 1577-edition or in the 1593-edition)—this title, in its 1593-edition, is

the only work by Peacham listed in the Lanham's bibliography.

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'transposition' of a phoneme within a syllable of a single word. These transformations are

due to ways of complying with the phonetical occurrences established in the spoken

language, usually contrary to the common origin of the word, or for adapting to the

vernacular what originally came from a foreign language—as it is also the case with the

word 'theater,' which is an adaptation from the Latin word 'theatrum.' The same occurs, of

course, with musica ficta and any of the three procedures of hexachordal change: they exist

in order to comply with needs of musical performance, which imposes inflections on steps

of the gamut (changing the designation of steps and creating new hexachords), and which

reach beyond the limits of hexachords (in order to virtually allow limitless possibilities of

elaboration)—all this is implemented even if it poses contradictions with the established sets

of theoretical explanations (the musical grammar) available during the Middle Ages and

Renaissance. Whatever the transformations are, 'metaplasm' never changes the signification

(or signified) of the word itself. That is the most significant difference, in fact, between

'metaplasm' and any of the three procedures of hexachordal change—for 'mutation,'

'permutation,' and 'transmutation' (as well the occurrence of musica ficta) all impose changes

in the signified of the word (for the hexachordal context of the step is forcibly changed). In

this sense, 'transmutation' is perhaps the only procedure that could produce a transformation

equivalent to that of 'metaplasm,' since there is an immediate return to the context of the

prevalent hexachord—nevertheless, the main step in 'transmutation' (the 'transmutant'-step)

is truly identified as an extraneous step (thus with a different signified).

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In fact, the distinctions between these figures are sometimes hard to define. Both

'metonymy' and 'synecdoche' are usually related, and classified within the same subtype of

substitutive figures as it happens with 'metaphor' and 'allegory.' 'Hypallage,' however, is

classified (together with 'metaplasm') as an ungrammatical use of language—which could

also be construed as some kind of vice of rhetoric. It seems therefore that, since in early

medieval theory musica ficta was equated with vices of rhetoric (by means of the word

'vitium'), 'hypallage' would be a better term to define the procedure named in the present

work as 'transmutation,' but the choice of 'metonymy' was manifold: because of its obvious

connections (morphologically and semantically) with the other procedures that signify

'change in the generic sense' (i.e., they all spring from the generic word 'mutatio'), and

because it is paired with 'mutation' (as 'metonymy' is paired with 'metaphor') as one of most

important and frequent procedures of hexachordal change.192 Finally, 'transmutation' (as

one of the possible Latin names used for 'metonymy') may be understood as a

denomination of a 'generic' figure that contains (i.e., embraces, or may be divided in) other

more specific figures such as 'synecdoche,' 'hypallage,' as well as 'metaplasm.'

In the light of what has been exposed above, it seems reasonable that those three

procedures of hexachordal change be named 'figures of solmization,' thus establishing a

clearer connection with 'figures of rhetoric.' When implemented, these

'figures of solmization' perform not only a musical task, but a rhetorical one: the task of

192 'Permutation,' given its rough nature of execution, does not happen nearly as frequent as the

other two procedures.

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persuading the audience of the subject and argumentations at hand, by means of references

to extraneous, new, or even unexpected ideas and imagery, even if only at the level of minute

detail, also serving to illuminate and broaden the audience's understanding of the figures

used by both disciplines.

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— CHAPTER 8 —

ISSUES OF TERMINOLOGY:FORGING TERMS, DEFINITIONS, AND CONCEPTS IN MODERN SCHOLARSHIP

(i) Generic Terminology: The Audience Considered

The previous chapters were dedicated to explanations of solmization and musica

ficta through its theoretical and practical contents, and involved the presentation of related

terms and concepts. However, some terms and concepts were subjected to little or no

discussion about origin or comparison between modern and early understandings (i.e.,

Middle Ages/Renaissance). In order to clarify the nomenclature of these previous chapters,

I will undertake the discussion of basic definitions of musica ficta, as well as of the term

'ficta-signs,' which were assumed earlier as a generic reference to the signs -quadratum (or

durum) and -rotundum (or molle), introducing some interpretive and speculative positions

along the way.

In a paper delivered at the American Musicological Society Meeting in Boston

(1998), Peter Urquhart argued against one trend in modern musicological practice that

produces rather artificial and decontextualized sets of rules. One of his main arguments

relies on the observation that the assembly of those sets of rules is often made without

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attention to the kind of public for which each individual rule was intended.

It must also be borne in mind that the rules that we have come to associate with the term musica

ficta were never stated as a set of principles in sources of the period. While these ideas stem from

the theory of the time, their assembly as a set of rules for performance or transcription is a purely

modern invention. It is useful, therefore, to reconsider the intended audience for each of these

various "rules," which is the primary intent of this paper. Briefly, the rules may be boiled down

to the following three categories.

1. the inflection of cadences: subsemitones; closest approach; "propinquity"

2. adjustment of melodic contour: avoidance of linear tritones; "una nota super la"

3. correction of harmonic problems; perfection of 5ths and 8ves; "mi contra fa"

I'd like to consider each of these rules in order, with the following firmly in mind: who was the

intended audience for these rules--the composer, or the performer reading his own part from

notation.

(Urquhart 1998, 2)

This assessment, however crucial, seems to have inadvertently dismissed another

possible audience for a treatise (and the guidelines or rules it establishes): the collective of

theorists, or even the theorist/composer. This audience should not be overlooked, especially

with regard to the Renaissance—from and for which Urquhart draws most of his

conclusions—and its Humanistic environment, when a large number of theorists (or more

generally, writers on music) were concerned with formulating new and original (personal

and independent) propositions, rather than merely repeating or expanding (through

quotation, paraphrase or gloss) on propositions by previous authors. An audience of

theorists (or even theory-educated and theory-concerned readers) can be viewed as a

metalinguistic audience, in the sense that, potentially consisting of readers/writers, it

exercises some degree of self-examination and self-criticism both when reading and when

writing. Since any given author is a member of this audience by default, one can assume the

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existence of a natural concern with structuring the text in such a way as to appease the

minute criticism of schooled peers—even when such an audience was not meant as the

primary public of the text. Thus, an audience of theorists exerts an indirect, interpretive

control over any given text, which may influence not only its reception, but (because of an

author's concern with that reception) may also influence the inception, production, and

completion of that text, or even its two most basic components: content and form (whether

or not these can be dissociated for analytical purposes). An author—who is writer, reader,

and self-critic at once—will choose between a number of conventions (both musical and

rhetorical), knowing that this choice may affect the acceptance (or even the survival) of the

propositions being made, and that this acceptance may be determined also by the form of

presentation (the content and assembly of those propositions). Of course, even if an author

chooses to avoid, disobey, or else contradict any number of conventions, many will have to

be followed, if not for the sole purpose of acceptance, at least to allow a minimum

understanding between author and audience through the text. Speculative, philosophically

informed writers of the Middle Ages and Renaissance (not unlike many modern music

scholars) may have been driven by particular interests in following certain conventions or in

establishing rules (aesthetic, and even ethical ones), which do not necessarily coalesce with

the practical concerns of either composers or performers.193 The learned and often obscure

language of medieval and Renaissance music theory suggests that the concerns and

193 For an appreciation of the role of musical theory, its speculative and ethical significances, cf.

(Lippman 1966).

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motivations of musical performers on the one hand, and those of musical theorists on the

other, were no less divergent then as now. That these differences should somehow have

concurred to produce a single cohesive and integrated strain of regulatory language

governing all musical situations—practical or theoretical—seems hardly likely. And yet,

modern ficta-scholarship has been grounded for the most part in precisely such an

historiographical construction. If there is a common substratum for communication

between theorists and performers (or other musicians, scribes, etc.), or even between

different theorists (whether they are speaking from the same or from different disciplinary

stances), that seems to lie within an understanding of rhetorical components, particularly

allegorical ones. The effectiveness of the rhetorical discourse (or more specifically, the

effective use of allegories or other rhetorical figures—generically speaking,

deviations of speech) is measured by its capacity to impress the mind of the audience, as

homogeneously and as subliminally as possible—no matter how learned or specialized are

the various segments of the audience. The noncoalescent differences between theoretical

and practical concerns—and perhaps even the impression of an obscure language—are

apparently due to interpretations of theoretical texts realized mainly at a literal level, or with

little attention to their various significances. Even though different audiences could (and

certainly did) produce different interpretations for a given text or situation, these differences

seem to lessen when the other three senses of exegesis (allegorical, moral or tropological,

anagogical or spiritual) are considered. Although this process of interpretation may

paradoxically allow individuals to impose readings and forge meanings of a personal nature

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(thus expanding the differences from one reader to the other), it also requires the use and

understanding of several commonplaces (necessarily embedded in the text), to which the

readers can (and must) collectively relate, and through which they can comprehend the

propositions made within the text.

Returning to the quotation above, Urquhart must be praised for having detected one

of the most significant problems with regard to interpretations of early texts: the modern

"assembly" of rules for musica ficta. This raises the notion of a forged "set of rules" that

has no correspondent in early music theory, but creates an inferential hierarchy that does not

seem to have existed between these so-called "rules," and that is made haphazardly available

to all kinds of modern audiences (such as modern scholars, modern performers, and

editors), usually without respect to the origin or intention of each "rule." In other words,

inspired by Urquhart's suggestions, one may state that both the assembly and the

application of rules are being implemented by modern scholarship irrespective of differing

audiences for each particular rule, or even irrespective of the context (musical, rhetorical, or

social) in and for which each rule was enunciated. But Urquhart's claim is only partially

true, for while one can hardly identify in a historical treatise one specific "set of rules"

exclusive to musica ficta, there are many sets that include ficta-related issues together with

general issues on solmization—at least from systematizations found as early as in Jacobus

Leodiensis's Speculum musicae (p. 1330, bk. 6, chs. 65–67; CS 2: 289–295; Bragard

1955–73, 6: 179–188) to Rhau's Enchiridion (1517, esp. chs. 3–4, ff. Ciir–Dijr), and Finck's

Practica musica (1556, tr. 1, ff. Biijr–Civ, Eiiijv–Fir, Fijr). It does not follow, however, that

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theorists were not engaged in producing a "set of rules," only that there were rather few

conspicuous attempts involving ficta-dedicated chapters.194 In any single treatise, these

'rules' are frequently scattered through different chapters dedicated to various topics—e.g.,

solmization, mutation, clefs, consonances and dissonances, or even counterpoint and other

composition-related topics, etc. Now, even if modern scholarship creates one such artificial

"set of rules," it does not invalidate the actual attempt of assembly, provided that intended

audiences are acknowledged, and that individual 'rules' do not take on the appearance or

intention of unexceptionable 'laws'; however more appealing and cogent the latter might be

for Western pedagogical approach. To be sure, Urquhart's starting point was an

identification of two different concepts (or definitions) of musica ficta: one (which he calls

the "old sense") representing direct formulations from medieval and Renaissance music

theory, and including only those steps that cannot be found in the recta-gamut; and the

other (which he calls the "modern sense of performer's accidentals") representing most of

modern musicological interpretation, and including any accidental inflections—even b

(equivalent to the recta-step -fa).195

194 One early attempt (of what modern scholars might identify as a "set of rules") is found in

Prosdocimus de Beldemandis's Contrapunctus, (1412–1425/28, ch. 5; Herlinger 1984, 70–94 [even

only])—also edited by Coussemaker as tr. 3, ch. 1 (CS 3:198–199).

195 Cf. the entry 'Musica ficta' in MGG 2 (6: 673–680) published in 1997, where Urquhart also

exposes some of the same concepts on which he lectured at the AMS meeting in Boston/98. The entry in

MGG 2 (6: 662–682) is co-authored by Jehoash Hirshberg ('Bis zum 14. Jahrhundert') and Peter Urquhart

('15. und 16. Jahrhundert').

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The two meanings of the term musica ficta, that of the 20th c. and of the earlier period, overlap to

a large extent, but each covers an area that the other does not [...]:

1) In the old sense [...] musica ficta includes notated accidentals. The

connotation of fictive as invented by the performer, imagined and therefore not

real or on the page, does not occur. Treatises that discuss musica ficta invariably

provide explicit accidentals, and most do not mention accidentals that are not

signed.

2) When used in the modern sense of performer's accidentals [...] "ficta"

includes musica recta pitches, specifically B . When one includes questions

about flat signatures, it is clear that modern discussions of "musica ficta" are

more often concerned with musica recta pitches than with musica ficta in the old

sense.

(Urquhart 1998, 1)

Urquhart is, in fact, elaborating upon similar concerns of earlier scholars, perhaps

voiced more conspicuously by Daniel Zager, in an article dedicated to discussing

solmization in fifteenth-century music.

The term musica ficta has frequently been used incorrectly to embrace all of the editorial accidentals

added to modern scores of Renaissance music. In fact, many of these editorial accidentals,

specifically many B s, may be explained and should be understood in terms of the standard system

of musica recta as delineated in the gamut, the theoretical framework by which the fifteenth-century

composer and singer defined musical space. Musica ficta, on the other hand, refers only to pitches

outside the gamut. The distinction is crucial, for while the fifteenth-century singer, and, by

implication, his modern counterpart, would normally avoid entering ficta hexachords unless

necessary, there was simply no reason to avoid the B s of musica recta. Thus, all editorial

accidentals are not equal, and it is critical that the modern editor make a conceptual distinction

between editorial accidentals representing musica ficta pitches and those representing musica recta

pitches.

(Zager 1989, 7)

Even if some modern scholars do not provide distinctions/definitions as explicitly as others,

a great many scholarly works have been careful in respecting and using the term 'musica

ficta'—though unfortunately not all—as it was conceptualized by medieval and Renaissance

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writers. With respect to works that do observe the early concepts of musica ficta, it must be

noted that most of them are found in the specialized literature of works devoted to the topic

of musica ficta, or in other related works by ficta-scholars.196 The situation, however, is

certainly not the same with regard to the bulk of music editions, to which Zager's and

Urquhart's criticism is rightfully aimed.197

In trying to formulate a merged concept, and considering the claims of the above

authors about medieval/Renaissance senses, musica ficta could be defined as a collection of

steps not pertaining to the recta-gamut, being used in order to obtain semitones or whole

tones where they could not be originally found, while wanting notated ficta-signs for the

proper identification of ficta-steps. However concordant with several assessments presented

earlier in the present work, if this definition is taken literally, and interpreted only via the

arsenal of modern terms and concepts, 'steps' (i.e., in the old sense) could be simply equated

196 One must include the invaluable production of Lowinsky, Allaire, Hughes, Bent, Karol

Berger, Christian Berger, Toft, and countless others, even if they fail to distinguish among the intended

audiences for each rule—something that Zager also fails to do. Urquhart's production should also be

included, with the exception that he duly proposes (as seen above) distinctions between 'rules' according to

intended audiences.

197 These editions of early music repertoire, not only tend to disregard the appropriate solmization

of a piece, in order to determine ficta-occurrences (whether or not these are effected by a ficta-sign), but

frequently take ficta-signs as accidentals applied only (or exclusively) to specific notes. Thus, the function

of ficta-signs as hexachord enforcers is concealed from the reader of those editions, and any inflections are

ultimately perceived as ficta-steps, even if they duly pertain to the recta-realm. This situation inadequately

contributes and furthers the understanding of musica ficta (and particularly of ficta-signs) as mere accidentals

in the modern sense.

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to 'pitches' (i.e., in the modern sense).198 In such a situation, b would always be

considered a pitch that has a correspondent in the recta-realm, and not in the

ficta-realm—i.e., equivalent only to a recta-step. Of course, this is not accurate, for while

the modern b can certainly correspond to the single recta-step designated as -fa, it could

also correspond to plural ficta-steps—e.g., -fa-ut, and -fa-sol.199

In fact, the early concept (or Urquhart's "old sense") of musica ficta, as exposed

above, needs to be further analyzed and rephrased, for it is composed of two different and

seemingly independent—however complementary—components (or definitions): one

'specific,' the other 'general.' As a 'specific' definition, musica ficta is a procedure through

which one (composer, scribe, theorist, or performer) makes a tone out of a semitone, or

vice versa. This definition, which implies an alteration within a given context (whether

melodic or harmonic), may apply to the necessity of substituting a consonance for a

dissonance, as well as to an aesthetic determination of obtaining some particular

consonance, even where there was no dissonance—in which case, it may be seen as a

198 In accordance with the terminological distinctions adopted at the outset of the present work:

'step' is here being used as a term that implies interval, as well as locations in the gamut, and is represented

by letter-plus-syllable designations—e.g, A-la, B-mi, C-fa-ut, etc.; 'pitch,' however, is the term elected in

this work only for modern, absolute, frequency-defined sounds, and is represented by letter-only

designations—e.g., A , B, C , etc.

199 A similar commentary was made by Margaret Bent, as the official respondent to the AMS

session in which Urquhart read his paper mentioned above. Moreover, it must be stressed that alone the

modern nomenclature does not allow one to determine whether a given pitch (e.g., b ) is equivalent to a

recta-step ( -fa) or a ficta-step (e.g., -ut). This applies to any pitch, not only those that bear accidentals,

but also those that do not in modern nomenclature (e.g., c' can be equivalent to c-fa within a -hexachord,

or equivalent to c-re within a -hexachord).

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definition that hinges on the concepts of causa necessitatis and causa pulchritudinis.

However, if an underlying default structure is not perceived (as it might within the narrow

scope of such a definition), a transformation from b-mi into b-fa (for whatever reason,

necessitas or pulchritudo) could be interpreted, for example, as belonging to the practice of

musica ficta, though these particular steps are commonly defined as recta-steps. As a

'general' definition, musica ficta is said to represent all those steps that are not found in the

standard array of steps (i.e., not found in musica recta)—this kind of definition does not

hinge nor depend on notions of necessitas or pulchritudo. While the 'specific' definition

emphasizes the transformational aspect over that of a default structure, the 'general'

definition does the opposite. The problem of comprehension then arises when any of those

definitions is individually generalized and assumed as some kind of 'rule' hierarchically

prevalent over the other; in fact, it is a problem of considering the audience in order to

achieve a more subtle comprehension of the texts.

Among those historical treatises that included discussions about musica ficta, not all

have included both of these definitions ('general' and 'specific'). An author's choice for one

or the other was apparently determined by necessity, in order to avoid ambiguities or

verbose clarifications; for example in sections of a treatise requiring one of the definitions,

but not the other. Where both definitions are discussed and enunciated in one and the same

treatise, they could be presented as complementary parts of a single concept, but much more

often complementarity was only implied. The latter case is observed when the two

definitions are presented in completely different sections of the treatise, with no explicit

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connection, or with any aspect of complementarity left exclusively to the reader's

interpretation. From the perspective of an author, whether such a reader's interpretation was

presumed necessary or unwarranted may have been a matter of which was the intended

audience of a particular assertion, or even of the whole treatise.200

Conjuncta est dum fit de tono regulari

semitonium irregulare aut de semitonio

regulari tonus irregularis, vel sic:

Conjuncta est appositio b rotundi aut

quadri in loco irregulari.

[...]

Ficta musica est cantus propter regularem

manus traditionem aeditus.

(Tinctoris 1495, ff. a iiiiv, [a viii]r; CS 4:

180, 184; Machabey 1951, 12–13, 28;

Parrish 1963, 14, 32)

Coniuncta is when an irregular semitone is

made out of a regular tone, or an

irregular tone out of a regular semitone,

or else:

Coniuncta is the apposition of b-rotundum

or -quadrum in an irregular place.

[...]

Musica ficta is song that has been produced

as a result of [i.e., outside of] the

regular tradition of the hand.

(my translation; cf. Parrish 1963, 15, 33)

Through these brief statements, Tinctoris provides both kinds of definitions (also

adding another about the use of ficta-signs), but keeps them completely unconnected;

although the additional component on the application of ficta-steps (the second entry on

'coniuncta') could even serve as a mediator. Two levels of interpretation must be noted: a

'micro' level, in which the two definitions are understood independently; and a 'macro' level,

in which there is only a single concept. The macro level, in which the two definitions would

be enunciated, possibly in one and the same merged sentence, is in fact a conceptualization

of modern scholarship; it is not generally found in historical treatises, and depends on a

200 The unconnected presentation of these definitions in two independent sections, or even the

choice of enunciating just one of the definitions instead of the other, may have served an author's intention

in producing treatises with either a speculative or a practical concern. The quotation from Tinctoris's

Terminorum musicae diffinitorium, given here for immediate reinspection, has also been included in

chapter 1 (ii), along with others providing those basic definitions of musica ficta.

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connection that only interpretation can provide.201 Properly merged, however, the two

definitions can convey a suitable and more complete definition (at least for the modern

understanding), not only of what musica ficta is, but also what it does, and/or how it may be

implemented.202 Even if the two definitions can be naturally made into components of one

201 In his Exégèse médiévale (1959–63), Henri de Lubac presented the four exegetical senses

(literal or historical, allegorical, tropological or moral, and anagogical or spiritual) mainly as means for

interpreting the Scriptures, although even within his work those exegetical approaches can be applied to any

kind of text (theoretical, musical, literary, etc.) whether belonging to sacred or to secular contexts. The

interpretation of which I speak with regard to the macro level is one that might benefit from each and all of

these exegetical approaches, and thus contribute to the identification of the intended audience of a treatise, or

just of a brief assertion.

202 As an evidence against the understanding being forwarded here, there is but one treatise that

has enunciated both definitions in a merged manner, in one sentence: Prosdocimus de Beldemandis's

Contrapunctus. Quoted below is the first paragraph of the last section (dedicated exclusively to musica

ficta) in Prosdocimus's treatise—in Herlinger's edition that entire section is given as chapter 5, and in

Coussemaker's edition as treatise 3 in one chapter. The quotation adopted the text from Prosdocimus's own

revision (between 1425 and 1428) of the original 1412-text, and the rephrasings or added words from that

revision are marked in boldface.

Hiis visis, aliquid de ficta musica, que huic arti neccessaria est, est pertractandum, unde ficta

musica est vocum fictio sive vocum positio in aliquo loco manus musicalis ubi nullomodo reperiuntur, sicut ponere mi ubi non est mi, et fa ubi non est fa, et sic de aliis

vocibus. De ista ergo ficta musica notande sunt hee regule, quarum prima esthec, quod ficta musica nunquam ponenda est nisi loco neccessitatis, eo quod in arte nichil est

ponendum, et maxime fict io, sine neccessitate.

(Prosdocimus 1412–1425/28, bk. 5; Herlinger 1984, 70, 72; cf. CS 3: 198)

Now that these things have been examined, we must study something of musica ficta, which is

necessary to this art. Musica ficta is the feigning of syllables or the placement of syllables in any

location on the musical hand where they are in no way to be found--to apply mi where

there is no mi and fa where there is no fa, and thus for the other syllables. Concerningmusica ficta, these rules must be noted, the first of which is this: that musica

ficta is never to be applied except where necessary, because in art nothing--least of all afeigning--is to be applied without necessity.

(Herlinger 1984, 71, 73)

(cont. ...)

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single concept, they are neither mutually inclusive, nor mutually exclusive, i.e., although they

can exist independently, the existence of one definition can be related to the other by

extension. An analysis of the conceptualizations that may have generated each definition

will shed some light on their differences and complementarity as well, and on how they

contribute to each other's clarification.

In the micro level, the two definitions are conceptually different: one ('general') is

static and speculative; the other ('specific') is dynamic and practical. The latter, 'specific'

definition (implying an alteration of a given default) describes an action, a procedure, a

practice: the actual modification from tone to semitone, or vice versa. Thus, it depends as

The entire section on musica ficta functions as a kind of addendum to the treatise, and the character

of the initial assertion suggests that the previous chapters are a consummate presentation. In light of that,

it appears that Prosdocimus regarded musica ficta as a practice of its own, differentiated from counterpoint

(perhaps even extraneous to it), although composers should know how to apply it in counterpoint. The

two basic definitions of musica ficta ('general' and 'specific') are followed by a warning against the overuse

of musica ficta. The assertion that "musica ficta is never to be applied except where necessary" has also

been used to develop the modern statement that the composer should not "write to many accidentals but

leave them to the performer" (Bent 1972, 77; 2002, 65). The origins of Bent's work ("Musica Recta and

Musica Ficta") can be traced back to the prominent works of Apel (1938, 1939, and 1950), Lowinsky (1945

and 1954), Hoppin (1953 and 1956), and also Parrish (1957) who first addressed the problems of the

so-called "partial" or "conflicting" signatures, "cautionary" signs, and non-notated signs. Its basically

through her convincing work, that the idea that 'in general ficta-signs would be better left unnotated' has

been developed, as if Bent was an outspoken defender of such an idea. In the same article, she stated that

"[Prosdocimus's] advice is not relevant to singers, schooled orally in a performing art, nor to the modern

editor who acts on the performer's behalf. Prosdocimus does not claim to help singers to solve problems;

he tries to eliminate problems before the singer has to tackle them" (Bent 1972, 77; 2002, 65). In fact, in

that particular paragraph, Prosdocimus is not addressing the notation or application of 'signs,' but rather it

is a much more generic statement that musica ficta (as a deviation from the gamut of musica recta) is to be

used sparingly, only where there is no other alternative. It may also be said that this assertion is aimed to

the audience of a treatise on counterpoint, not of a treatise concerned with musica practica.

For all the modernity of Prosdocimus's presentation in its approach and tentative

comprehensiveness (although clearly separating musica ficta from counterpoint), it is not surprising that his

text has been used as a support to modern concepts and presentations.

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much on motion, as on active intention of change, and conveys a concept that is both

dynamic and practical in essence. The 'general' definition, however, denotes an abstraction:

the delimitation of steps within two different but correlated systems (recta-gamut and

ficta-gamut), hence establishing the conceptual existence of crystallized and hermetically

conceived frames.203 Obviously, the delimitation and establishment of frames per se does

not depend on motion, and is intrinsically passive, for it is founded on applying

preestablished designations for each step. Thus, it conveys a speculative concept, by force

of being founded in an abstraction, as well as it denotes a static condition, by force of its

motionless, passive character.204

203 The notion of 'static,' 'crystallized and hermetically conceived' frames can be related to the

recta-gamut in its clear limitations and stillness, since theoretically it cannot be expanded and at the same

time keep its function and denomination as 'recta.' At the same time, the ficta-gamut, offers an speculative

conceptualization that allows for expansion, but whose limitations are given by the preexisting

recta-gamut. The two gamuts, in fact, cannot be seen as subsets of one another, but as parallel and

interdependent sets—much like the 'general' and 'specific' definitions.

204 The association of those particular qualifiers ('general' and 'specific') with the two micro-level

definitions ('speculative' and 'practical,' respectively) may, at the same time, be understood as a paradox.

The qualifiers are here being applied because of the results each of the definitions impose on the merged

macro-level concept of musica ficta. If the practical concept, primarily dependent on the idea of change, is

divested of principles of regularity versus irregularity (i.e., default versus its alteration), then it can be

applied indistinctively to recta- and ficta-steps, and thus may be considered 'more general.' If the

'speculative' concept is more dependent on the pre-definition of (and comparison with) a structure such as

the recta-gamut, which is a restriction in itself, than on the breadth of expansion of the ficta-gamut (which

does not exist independently), then its qualification can also be understood differently, and thus it may be

considered 'more specific,' because 'restrictive.'

286

Johannes de Garlandia (fl. ca. 1240), in his Introductio musice, was once identified

as the first author to have explicitly used the term 'falsa musica' (i.e., musica ficta), defining

an intentional and justified change in the quality of a step (thus, a 'practical' definition).205

Falsa musica est, quando de tono facimus

semitonium, et e converso.

(Garlandia med. 13th cent.; CS 1, 166)

False music is when out of a tone we make

a semitone, or vice versa.

(my translation)

However, Christopher Page (1991, 96n) denies Garlandia's position as the first

author to have used the term 'falsa.' Page's view is based on the appearance of the term

'falsa' in two treatises: Summa musice, attributed to the double authorship of Perseus and

Petrus, according his own edition of 1991; and Carmen de musica cum glossis (?13th

cent.) attributed to Alexander de Villa Dei, according to Seay's edition of 1977—Page dates

both treatises to ca. 1200. In the latter treatise, the appearance of the term 'musica falsa'

implies the existence of a prior, well-known definition, although one cannot tell whether this

definition would have been formulated in a written form, or just divulged orally—cf. (Villa

Dei ?13th cent.; Seay 1977, 19). In the case of the Summa musice, the authors named by

Page do not go beyond the use of 'falsa' as a mere adjective (i.e., as a qualifier with no clear

terminological intention), and suggest that although 'false' procedures and 'false' intervals

may exist, 'musica falsa' "should be scrupulously avoided" (Perseus and Petrus ca. 1200,

205 The attribution of primacy of such an use of the term 'falsa musica' had been given in

Margaret Bent's entry in the first The New Grove Dictionary—cf. (NG 1, 12: 803, s.v. 'Musica ficta'). The

quotation from Garlandia's treatise has also been included in chapter 1 (ii).

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ch. 23; Page 1991, 122 [trans.], 199 [Latin]).206 Thus, Perseus and Petrus imply that

musica ficta would be unacceptable both as a regular practice and as an institutional

concept. Even if Johannes de Garlandia was not the first to use the term 'falsa,' and his

definition was a restatement of 'practical' definitions that existed before, he may still be

responsible for providing a formal definition of musica ficta by conspicuously utilizing

'falsa musica' as a designating term. In fact, Garlandia employed the term 'falsa' beyond its

use as a mere adjective, as previous theorists did, and conferred to the term 'falsa musica' a

musico-lexicographical status.207 However, attempts to account for, and above all validate

the practice of musica ficta appear as early as the second half of the ninth century,

206 Cf. also (Perseus and Petrus ca. 1200, chs. 15, 21, 23, 25; GS 3: 221 [formae for falsam],

235, 238–239, 243; Page 1991, 177, 195, 199–200, 206). Formerly, this treatise was attributed to

Johannes de Muris, based on the inscription given in Gerbert's edition (GS 3: 190–248). Later this

inscription was challenged and an anonymous author was claimed (sometimes referred as Pseudo-Johannes

de Muris). As mentioned earlier in chapter 1 (note 34), Page's date (ca. 1200) may also be challenged on

the basis of a number of untimely references to Aristotle's (through citation, gloss or paraphrase), which

Page himself identifies, but which may be unusual for such an early date in the acceptance of Aristotle's

auctoritas on the part of the Church, which would enable his works to be so openly used. Although the

Lexicon musicum Latinum medii aevi has kept a different date for the treatise (i. 1274–1312), Page's

contention has been accepted by Margaret Bent in the new edition of The New Grove Dictionary, together

with another early use of that term, stating that "[t]he earliest known use of the term musica falsa is in a

late 12th-century didactic poem, describing variable hexachord steps (I-Rvat lat. 1346; [from] an

unpublished edition by Smits van Waesberghe [...])" (NG 2e, s.v. 'Musica ficta,' §2 [ii]).

207 In fact, although Page's dates for those two treatises (Perseus and Petrus's and Villa Dei's) may

be debatable, that may be less relevant in tracing the origins of 'falsa,' for many earlier theorists employed

the term 'falsa' as an adjectival reference to those step alterations that fall within explanations of 'musica

ficta' and its practice—e.g., (Anon. SE a. 900, pt. 1; GS 1: 173, 175, 177; PL 132: 983, 985, 988;

Schmid 1981, 61, 65, 72); (Anon. Comment. Microl. 1070/1100; Vivell 1917, 34, 35); (Guido d'Arezzo

1026–28, ch. 10; B-Br II 784, f. 8v; GS 2: 10; PL 141: 389–390; Waesberghe 1955, 133–134); (Aribo ca.

1070's; Smits van Waesberghe 1951b, 13–14; GS 2: 203; PL 150: 1313–1314); (Affligemensis ca. 1100,

ch. 2, 7, 21, 22; GS 2: 233, 237, 257, 259, 260; PL 150: 1394, 1398, 1422, 1424, 1425; Waesberghe

1950, 52, 65, 133, 139, 143)—some of the evidences from earlier authors were presented in chapter 1 (ii).

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frequently introduced under the classification of 'error' or 'corruption' (or literally, a 'vice,'

from the Latin noun 'vitium'). In fact, the term 'vice' is one of the earliest and most

significant terms employed in the presentation and process of defining musica ficta, usually

in terms of the 'practical' perspective explained above. These early definitions and

validations of musica ficta (i.e., vitium) embraced not only issues that were purely musical,

but philosophical and rhetorical as well, for the same word serves as an opposite to 'virtue'

('virtus'), and as a reference to 'vices of language.' This can be conspicuously observed in

the quotation below, from Scolica enchiriadis. (Note, however, that in Erickson's

translation, the word "vitia" has been translated as "errors," thus concealing the connection

with the rhetorical concept of 'vices of language,' although it is openly stated by the

anonymous author.)

M: Limmata ergo haec non plena spacia

vocari solent et per ea interdum vel modus a

modo transfertur vel per eadem restituitur,

sicut in cantibus satis observari poterit.

∆ : Num pro vitiis ea reputabimus?

M: Vitia nimirum sunt, sed sicut barbarismi

et soloecismi metris plerumque figuraliter

intermiscentur, ita limmata interdum de

industria cantibus inseruntur.

(Anon. SE a. 900, pt. 1; Schmid 1995,

69–70; GS 1: 176–177; PL 132: 986–987)

M[aster]. It is customary to call these

less-than-whole intervals limmas.

Sometimes through them one mode is

changed into another, or the original mode is

restored. This can often be observed in

chants.

D[isciple]. We do not regard these things as

errors, do we?

M[aster]. To be sure, they are errors, but

just as barbarisms and solecisms are

frequently intermixed in verses for poetic

reasons (figuraliter), so limmas are

sometimes deliberately introduced into

chants.

(Erickson 1995, 41; cf. Atkinson 1988, 194)

Besides the marked statement by the Master, relating those musical 'vices' to

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rhetorical counterparts (specifically "barbarisms and solecisms"), the question by the

Disciple implies moral and philosophical contexts which are not denied by the Master, only

expanded to include the context of rhetoric. With respect to the definition of ficta, the text

asserts that 'vitium' is a procedure through which one can obtain a semitone where only a

tone would be originally found (i.e., according to the standard established through the

Daseian notation), or else a procedure that can restore the original structure either by means

of imposing a semitone or a whole tone. Since Scolica enchiriadis is a treatise that shows

musica practica concerns (at least in the section from which the quotation was excerpted), it

is appropriate to have a definition of a 'practical' nature such as the one above, although with

hints of 'musica speculativa' both in its subliminal mention of a standard from which the

'vice' is deviating, and in the open references to rhetoric.

Significantly, in defense of the notion that practical procedures precede theoretical

explanations, the 'practical' (specific, dynamic) concept seems to have appeared and have

been emphasized already in the oldest sources, while the 'speculative' (general, static) seems

to be a later construction, designed to adapt an already existing concept of change to the

change in standards of solmization. Now, despite the dependence of something 'ficta' on a

pre-definition of something 'recta,' it is the need for something 'ficta' (i.e., for alterations of a

standard) that precedes the qualification of something through the term 'recta' (the

standard). In other words, if there was no need for ficta-occurrences, the standard structure

in use would be the only one available in reality, and thus it would need no definition,

distinction, justification, comparison, or even validation; it would be 'general' and 'specific' at

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once, and therefore also 'speculative' and 'practical' at once.208 These considerations allow

us to formulate perhaps one last (macro-level) definition of musica ficta, combining both

facets ('practical' and 'speculative'): musica ficta is a practical means through which one can

obtain semitones and whole tones within a different theoretical array of steps than the ones

available solely via a default standard for a given musical (or theoretical) text.

These assessments—in which the 'practical' perspective has been interpreted as a

prior element—would seem to imply some kind of hierarchy between the two micro-level

definitions. Although this may be true, both chronologically and in a literal sense (from the

standpoint of their enunciation in early treatises), the division proposed above is also

interpretively pedagogical, for the two micro-level definitions are virtually inseparable by

force of their complementarity—as mentioned above.

As for the merged definition, one of its corollaries is the understanding that musica

ficta deals primarily with the aural identification of intervals within a hexachordal structure,

and not of unrelated steps or specific pitches—and certainly not with the identification of

the absolute (frequency-defined) pitches of the modern era. As has already been noted, this

identification of intervals was not only informed by the Guidonian hexachordal paradigm

(T-T-S-T-T) that served as means for solmization, but was also embraced by way of the

letter-plus-syllable(s) designations through which theorists defined places within the gamut.

These designations are, in fact, conjunctions that both preserve and merge the notion of

208 It is not surprising that musica recta may be discussed both as a symbol and as the only

means for the musical expression of godly things.

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intervallic variable (via hexachordal step-syllables), and the specificity and regularity of

sounds (via step-letters)—again the 'dynamic' versus the 'static.' Thus, musica ficta , in all

its aspects (procedures, use, existence, and speculative validation), is virtually inseparable

from solmization, even when this solmization does not follow the Guidonian tradition, or

even if it does not involve hexachords.209 In this light, it is first toward solmization that the

scholar must look in order to ultimately interpret the modern pitch-equivalent content of a

composition of 'early' music. As Margaret Bent has reminded us, modern scholars should

note that early notation was not as intentionally prescriptive as the modern notation

employed to transcribe medieval and Renaissance music.210

It is the modern transcription that has traditionally been treated as our default, as when we refer to

"the notation as it stands," or at "face value," despite changing standards in editorial practice. After

considerable editorial experience, it is now my conviction that so to treat it is a greater

disfigurement and source of misprision than to start from the other end, as I now advocate. It is

obvious that their starting point for these determinations, their access to the music, was not from a

modern transcription but rather through singing from their manuscripts and prints. Early notation

provided a weak intervallic default organization by clef and signature, but because it was

incompletely prescriptive of pitch (hence "weak default"), the performer expected to arrive at actual

sounds by some means besides prescriptive notation.

(Bent 1996, § 5)

Some scholars have, in fact, misunderstood (or even ignored) the importance of this

"incompletely prescriptive" character of early notation, and jumped too soon to the

209 For example, in the case of the above quotation from Scolica enchiriadis, one cannot speak of

a gamut in Guidonian terms, but of an array of steps derived from the so-called 'daseian' arrangement, which

was as standardized as its recta counterpart—at least, within the cohesiveness of those 'daseian' propositions.

210 Also in other essays, Margaret Bent discusses the equivalence (or its absence) between early

and modern notation, and the latter's inadequacy to provide all the elements necessary for an understanding of

the original musical text—cf. (Bent 1994b, esp. 373–385; 1998, esp. 15–26).

292

conclusion that it would be enough to provide added accidental-inflections (in highly

prescriptive, modern-notation scores) through a simple application of rules of counterpoint.

With regard to counterpoint as a solution to ficta uncertainties, Bent's statements, always

carefully worded, may have even contributed to this misunderstanding by other modern

scholars and editors. Virtually in all of her writings dealing with musica ficta, she has

struggled to mark her position and to indicate (in a much more clear discourse than previous

scholars) that musica ficta must always be understood and solved in the context of

counterpoint—the following quotation, from a fairly recent essay, may serve as illustration.

It is in respecting and reconciling melodic principles and the rules of counterpoint that ficta is

necessitated; I have tried to show that ficta needs to be viewed in the context of counterpoint as a

whole, and not informed just by precepts specifically labelled as ficta.

(Bent 1996, § 3)

Furthermore, although she does not dismiss the importance and attention to

solmization, she explicitly (and to me paradoxically) dismisses its role as a determinant of

musica ficta.211

I never meant to claim (as Zager implies but does not state) that solmization can resolve

counterpoint/ficta problems. I do not share his dependence on solmization to determine

counterpoint. Rather the converse: contrapuntal decisions, once made, can be expressed in terms of

solmization, the nearest they had to a precise language in which to conceptualise and name sounds.

But since they stretched the system to cope with all eventualities, so that anything could be

solmized by extensions and disjunctions, the criterion of easy solmization is not a valid arbiter of

which sounds are or are not possible. To argue a particular solution from solmization is to let the

tail wag the dog. I wrote: "Hexachords provide a functional context for semitone locations which

have been predetermined by musical considerations, but they do not in themselves determine what

the sounds will be. The hexachordal voces are the means by which those sounds become

211 Similar claims, as the one quoted here about the role of solmization, were stated by Margaret

Bent in her response to Peter Urquhart's paper (1998) mentioned above.

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practically accessible in vocal polyphony, just as, by analogy, fingering is the means by which

small groups of notes are physically negotiated on instruments." Hexachordal thinking permeates

their terminology. It guides us away from the notion of "inflections" of individual notes and into

that of small scalar segments (sometimes projected as tangents from the scala of musica recta) that

accommodate and articulate semitones, the need for which is pre-determined on contrapuntal

principles. It cannot in itself solve individual ficta problems just as, conversely, no ficta solution

can be rejected on grounds that it can't be solmized.

(Bent 1996, § 18)

Of course, solmization cannot "determine counterpoint," but it does determine the

reading of a composition, and therefore may be used to inform and even actively contribute

to creating (composing) the intended musical structure.212 There is also no doubt that

counterpoint (and its own precepts) should weigh in the final evaluations of ficta, as much

for the modern musicologist, editor or performer, as it may have weighed in decisions made

by composers and perhaps also by scribes. However, as far as the original performers are

concerned, there should be no doubt that a heavier weight was placed on solmization, for the

sake of identifying steps (thus including ficta-steps)—at least at the basic level of

identification that performers were supposedly capable of executing. Also, both the

composer and the scribe seem to have had no alternative but to abide to these basic

procedures, language, and reading-patterns of their peer performers. Thus, in the present

work I have argued that solmization must have precedence over any other decision when the

modern scholar, editor, or performer is faced with a piece that utilizes ficta-signs

212 Thus, solmization and hexachordal syllables are neither limited to being instruments of

description (designation) of steps, nor restricted to passively serving as means of accessing the tone-content

of the composition, but also serve to further the understanding of musical structures. Canons and other

imitative structures have already been noted and accepted as classic examples in which solmization and

hexachordal syllables are used in this sense, thus interfering in compositional processes, to their

benefit—cf. (Leech-Wilkinson 1984).

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properly.213 At the same time, as stated in previous chapters, one must bear in mind that

extant medieval and Renaissance manuscripts (as well as printed editions) are not exempt

from errors of all sorts. For most of those errors, of course, whenever polyphonic music is

concerned, probably the best yardstick would be one that is marked with the paradigms of

counterpoint, more than those of solmization. This is the only exception; in all other cases

solmization ought to have precedence. In any case, it is not the performer, reading from his

individual part (whether or not able to see the separate notation for the other voices), who

has the responsibility for compositional corrections, deviations, or enforcing any

contrapuntal rule the composer may have decided not to observe, or the scribe may have

notated in some ambiguous manner. Naturally, modern scholars do not necessarily have to

agree with this interpretation, even if they have defended that musica ficta may be defined as

"part of the performer's art."214

In order to further assess what role counterpoint versus simple solmization may

have had in the process of identifying as well as determining steps (in performance), one

must bear in mind some issues concerning the different levels of erudition and musical

education of early theorists, composers, scribes, and performers in general—including, but

not limited to interpretations of historical, rhetorical, as well as societal perspectives. Thus,

the understanding of historical concepts and their application can only be solved by means

213 In this respect, the explanations contained in this dissertation have considered primarily the

Guidonian model, because it allows for clearer presentations of concepts and procedures, which can be

generalized further to other kinds of solmization paradigms.

214 Cf. Margaret Bent's statement in (NG 1, 12: 803, s.v. 'Musica ficta').

295

of interpretive approaches, informed by the use of an appropriate terminologies that do not

conceal the historical meanings and subtleties from the modern scholar, nor impose

untimely meanings to interpretations. In accordance with this analysis, it is imperative to

discuss the adoption and application, in the present work, of one particular item: the term

'ficta-sign' instead of 'accidental,' or of other possible terms.

(ii) Particular Terminology: Accidentals Versus Ficta-signs

This section will discuss conceptual impediments to employing the term

'accidentals,' first considering purely musical issues and misapprehensions generated by the

meaning of the term in modern usage, then inquiring into the philosophical significance of

the term, illustrated by a speculation with regard to its understanding and use in Marchettus

da Padova's two main treatises (Lucidarium and Pomerium). The term 'ficta-signs' shall be

discussed and defended later in section (iii), where other alternative terms—'hexachord-

signs,' 'syllable-signs,' 'interval-signs,' and 'solmization-signs'—will also be discussed. First,

however, some considerations about the existence of a 'generic term' must be observed.

More specifically, the proposition of a 'generic term' referring both to fa-signs ( ) and

mi-signs (whether , , or other variants) is controversial and arbitrary in essence. To be

sure, there seems to have existed no conspicuous intention of creating a generic term, either

in medieval or in Renaissance theoretical writings. Thus, one could argue that an attempt in

modern scholarship to forge a generic term may be unsubstantiated (because there is no

296

historical evidence of any such term or of any intention of speculatively defining one), or

fallacious (because it may lead to a crystallization of concepts that was not intended either in

early theory or practice), or minimally deceiving (because its creation would only be serving

a rationale proper of modern scholarship and of reductionistic trends). At the same time,

demands for a generic term seem justifiable especially in the case of the present work, where

definitions and terms are necessary to carry out the discussion, provided these definitions

and terms are not taken as fixed and inalienable entities, but as signs or abbreviations of a

larger concept. The need for meticulously defined generic terms, that can be used

ubiquitously, is truly a modern one.215 The modern compulsion toward lexical terms

represents (and is driven by) a paradoxical ideal, whose intention is to ally the

comprehensiveness of the 'universal' to the minutia of the 'individual.' In philosophical

terms, this trend purports the creation of terms that can be 'universalized' and granted an

'extensional' significance, even though they can only act 'individually' and 'intensionally.' It

is in this light that a modern coinage of a generic term for the signs of fa and mi needs to be

understood.

The term 'accidental,' according to its modern concept and usage in music, refers to

signs applied to individual pitches, and will necessarily alter the sound of the pitch in

215 Musical lexicalization seems to have become a major concern among scholars only after

Classical Encyclopedism, even though lexicons containing musical terms were being produced at least since

the times of Varro's Disciplinarum (1st cent. B.C.), and even though Tinctoris's Terminorum musicae

diffinitorium (1495) is commonly regarded as a watershed in this matter.

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relation to a given default without the sign.216 At least in terms of the standards set by

modern notation, an 'accidental' does not alter significantly the overall tonal structure of a

piece, unless its sign is meant as a key-signature. As for those 'signs of early music,' even

when they impose sound-inflections to specific steps (which is not always the case), they

not only imply a change in the underlying hexachordal structure, but may also affect the

understanding of the mode itself (whether or not they are found in signature positions).

Thus, the modern use of the term 'accidentals' for these 'signs of early music' leads to a

largely mistaken assessment: one assuming that their concepts (of 'accidentals' and of 'signs

of early music') can be equated. One of the elements that may have contributed to this

misconception appears to have been drawn from an equally mistaken interpretation that

musica ficta was primarily the expression of non-notated (or unwritten) signs. For instance,

the hypothetical example illustrated in FIG . 8 .1 could be described as containing a leap from

-fa to e-la-mi, where a sign (originally meaning a fa) has been provided only for the b, but

none for the e. If the tritone is to be avoided, and it is also accepted that b must be translated

as b by force of its solmization as -fa, then e will have to be translated as e ' (since to

avoid the tritone it must be solmized with the syllable fa as well).

216 Of course, modern 'cautionary accidentals' are usually not assessed under this category of

mandatory alteration, since they may be interpreted as preventing an alteration from occurring. However,

one may also understand that, if an alteration needs to be prevented, then a previous alteration is being

understood (even if momentarily, and even if mistakenly) as a default. In the latter sense, the cautionary

accidental would also be acting as a further alteration (or perhaps a 'de-alteration') of that altered, new

default, even when the cautionary accidental serves only to warn about the still valid, initial default

established by a key-signature or its absence.

298

8

: ut misol 3

la sol= [fa=]:[=re] =ut

3 3 fa mi fa

[=la]=solsol mi= [re=]

3 mi fa mi ut re ut

FIGURE 8 . 1 - Overuse and underuse of signs ('accidentals' versus 'ficta-signs').

In fact, when the fa-sign is used in a signature position like this, it is creating what

may be called here a ficta-signature—its function is to establish a new setup of

hexachords.217 If no ficta-signature was given, there would be only three possibilities for

reading the melodic gestures: the three basic recta-hexachords ( , , ). As a signature is

given, it shifts the expected three-hexachord group to new setup, which in the case of one

fa-sign on b will move that group down a fifth into the molle-family, thus establishing a new

group of three hexachords: -hexachord, -hexachord, and -hexachord.218 At the same

time, two factors could be considered in the above example: (a) the first melodic gesture (six

notes, from F to b) would denote the -hexachord whether or not there was a fa-sign; (b) if

that b is going to be solmized as -fa even without the sign, and the tritone should be

217 Of course, the function of a ficta-signature derives from the function of a 'sign of early music,'

which is primarily to impose a hexachord; or else, to impose a solmization-syllable on a specific

step-letter, and therefore impose the hexachord to which that letter-plus-syllable pertains.

218 If the signature had presented one fa-sign on b, and another fa-sign on e, then the expected

solmization would move down yet another fifth into the molle-family, thus the -hexachord, -hexachord,

and -hexachord would be the ones expected to serve for the solmization of the entire melody. The more

fa-signs in a signature, the deeper into the molle-family the expected hexachords for solmization will get,

but always maintaining the expectancy of three hexachords, unless another hexachord is imposed, by

placing another sign within a melodic gesture.

299

avoided, then e (seventh note in FIG . 8 .1) will necessarily have to be solmized as e-fa

according to the -hexachord. In this situation, the signature fa-sign seems to be even

redundant, for the solmization would be the same whether or not it was given, provided the

hexachordal indications promoted by the melodic gestures are observed. Thus, FIG . 8 .2

below shows the same example as before, with the same solmization, but without the

fa-sign.

8

: ut misol 3

la sol= [fa=]:[=re] =ut

3 3 fa mi fa

[=la]=solsol mi= [re=]

3 mi fa mi ut re ut

FIGURE 8 . 2 - Absence of signs ('accidentals' versus 'ficta-signs').

Situations like these are part of the reason for the perpetration of the modern notion

that musica ficta refers to accidental-inflections where no signs were originally notated.

Such a notion implies that the early signs would indicate no more than an alteration of a

specific pitch, and not that they could act as harbingers of a change in the solmization of a

particular melodic gesture—notedly, according to hexachordal structures. This modern

understanding is obviously dependent upon the assumption that the same conceptual value

of modern 'accidentals' can be applied to those 'signs' for musica ficta, therefore concealing

their hexachordal meaning. In fact, it is not only by equating their concepts that their action

(or their value) is equated, but by equating their names; i.e., by referring to those 'signs of

early music' simply as 'accidentals,' the latter term imposes on the former its concepts and

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actions. In the examples above, notice that the pitch e is being considered an equivalent to

the ficta-step e-fa, solmized according to a ficta -hexachord. Also, the pitch b is

equivalent both to the ficta-step -ut ( -hexachord) and the recta-step -fa ( -hexachord),

whether the fa-sign was deliberately provided or not. It is clear that both ficta- and

recta-steps (equivalent to accidental-inflected pitches) can be obtained with or without

'signs' attached to them, provided the hexachords are solmized according a proper reading of

the melodic gestures. Thus, 'accidentals' cannot be equated either with 'ficta-signs,' or with

'ficta-steps' (whether they are obtained through the use of ficta-signs or not); or in the words

of Peter Urquhart:

Musica ficta does not equal non-notated accidentals, and statements about musica ficta by theorists

must not be taken as statements about non-notated accidentals.

(Urquhart 1998, 12)

The term 'accidental' refers only to isolated pitch occurrences and inflections, rather

than step occurrences and changes within the larger scope of hexachords. The unwarranted

use of the modern term 'accidental' in place of those 'signs for musica ficta' allows for an

unfolding of misapprehensions about musica ficta (its concepts, definitions, functions, and

procedures). The three quotations shown below shall serve as a sample of statements that

may mislead modern scholars, especially those whose work does not place musica ficta and

solmization under strong scrutiny. Statements like these are included in works whose

objective toward musica ficta is only to provide an overview, thus influencing a number of

readers into misconception.

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There exists a crucial misconception about music of the century before 1550. It is often thought

that it was performed, as it was notated, largely devoid of accidentals, that it confined itself almost

exclusively to the modes, to scales mistakenly thought of as having uninflectable degrees.

Nothing could be further from the truth. Music of the Renaissance can display quite remarkable

chromatic colouring, and also far more of what might now be thought of as 'tonal' usage than this

misconception would admit. However, the inflections involved were rarely notated, since it was

expected that the music would be sung by performers intimately acquainted with a complicated

series of conventions for introducing chromatic alterations.

(Routley 1985, 59)

————————

The term musica ficta is now often used loosely to describe intended accidentals left unwritten

in the original manuscripts or prints of music from before about 1600 but added in performance or

editing. [...].

Although the theoretical definition of musica ficta remained constant in the years before 1600,

the degree to which unwritten accidentals were admitted into practice and sanctioned by theorists

changed greatly over time. This change is highly significant, because the addition of intended but

originally unwritten accidentals is the principal matter of concern to modern scholars investigating

musica ficta. No single formula for applying accidentals to all types of music has been found, nor

is one likely to be.

(NHarvard 1986, 517, s.v. 'Musica ficta')

————————

The term musica ficta has acquired two separate but related meanings. In today's casual parlance, it

refers to the application by editors and performers of accidentals (sharps, flats, naturals) that are not

notated in the sources themselves. For musicians of the fifteenth and sixteenth centuries, the term

referred specifically to those notes that fell outside the Guidonian hand [...].

(Atlas 1998, 328)

Even if some of these statements are careful enough to apply the terms "loosely" or

"casual parlance" as qualifiers, they do not explain adequately the terminological and

conceptual equation they implicitly establish between 'accidentals' and 'signs for musica

ficta,' and thus they help to advance the mistaken generalization that 'ficta-signs' were left

unwritten as a default practice. In this respect, Karol Berger's paradigmatic work is again to

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be praised, for he calls direct attention to the inaccuracy of such definitions at the outset of

the section on "Written and Implied Accidental Inflections"—the last in his work.

In popular, and as should be clear by now not quite correct, musicological usage the term musica

ficta refers to accidentals implied by the music of the Middle Ages and the Renaissance, but not

written down in the sources. [...]. And yet, the fact that not all accidental inflections called for by

the music of our period were expressly notated is the main reason why musicologists are interested

in problems raised by musica ficta [...].

(K. Berger 1987, 162)

By using the term 'accidental,' as pointed out above, these statements ultimately

shelter the assumption that the concept and understanding of ficta-signs is virtually

equivalent to that of modern 'accidentals.'219 To be sure, even if a term such as 'accidens'

was used in historical treatises, it was never exclusive to those signs for musica ficta.220 A

conspicuous use of this philosophically charged term (together with other morphologically

similar terms) can be seen in the Pomerium (1318/19) of Marchettus da Padova, where it

was utilized to characterize a number of different musical signs. The presentation that will

follow the quotation (discussing possible translations of his text) is designed to place

Marchettus's use of 'accidens' and others terms (such as 'essence' and 'proprietas') within

219 In this respect, Karol Berger's work (entitled Musica ficta: Theories of Accidental Inflections

in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino) is no exception, despite his many

insightful and enlightening assessments.

220 Cf. the illustrative survey of quotations for the term 'accidens' given in the Lexicon Musicum

Latinum Medii Aevi (Bernhard 1995, 2: 24–27). In all those instances, one can conspicuously observe the

philosophical meaning of term 'accidens' (and similar), which is contextualized toward several musical

procedures and concepts, including issues concerning fa-signs as well as mi -signs, modes, mensural

notation, etc. The term also appears in the treatise by Boethius (a. 510, bks. 1 and 2; GB-Ctc R.15.22

(944), ff. 13v, 14 r, 28 r; PL 63: 1176, 1196; Friedlein 1867, 195, 196, 227), whose citation, surprisingly,

has not been included in the Lexicon for this particular entry.

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an Aristotelian philosophical context, which will then serve as basis for the subsequent

discussion concerning the application of 'accidental' in musica ficta.

Quoniam, dicente Philosopho in

prooemio de Anima, accidentia multum

conferunt ad cognoscendum quod quid est, id

est, per cognitionem accidentium devenimus

in cognitionem essentiae rei. Cum igitur in

praesenti opere nostrae intentionis sit

cognitionem tradere per rationes essentiae

musicae mensuratae, igitur primo de

accidentibus sive de accidentalibus

concurrentibus in musica mensurata

principaliter est tractandum, deinde de

essentialibus musicae praelibatae.

Quantum ad primum, est sciendum quod

omnia praeter notas, in quibus solum

essentialis ratio consistit musicae, ut

demonstrabitur Deo dante, sunt accidentia

sive accidentalia concurrentia in ipsa musica

mensurata rationibus infra dicendis. Cuius

modi sunt caudae, proprietates, pausae,

puncta et quoddam signum quod a vulgo

falsa musica nuncupatur.

(Marchettus 1318/19, bk. 1, pt. 1, tr. 1;

Vecchi 1961, 39–40; GS 3: 123–124)

Since, [as] the philosopher [Aristotle]

said in the preface to De anima, that

'accidents' confer much to the knowledge of

what it is [of what a thing is], that is,

through the 'accidents' of knowledge we

arrive at the essential material [the 'essence']

of knowledge. Thus, since in the current

work our intention may be [or, is] to bring

knowledge through the understanding [or

else, theory] of the essence of measured

music, then first and more importantly one

must examine the 'accidents' or the

'accidental occurrences' in measured music,

and later the aforementioned 'essences' of the

music.

Of the first, be it known that all, except

notes, in which only the essential reason

consists of music, as will be demonstrated

later by [the will of] God, are 'accidents' or

'accidental occurrences' in measured music

itself, by the reasons indicated below. Of

such kind there are caudae [i.e., tails, or

stems], proprietates, rests, dots [of division],

and a certain sign called falsa musica by the

populace.

(my translation; cf. Renner 1980, 7–8)

The Latin word 'accidens, -tis' is originally the present participle active of the verb

'accido, -cidere, -cidi' (to happen, to occur, to turn out, to befall, etc.); but it could also be

used as a verbal adjective or as noun, as in Marchettus's text. Derivatives of this word are

found in the adjective 'accidentalis, -e,' and in the feminine noun 'accidentia,

-ae'—generated from the nominative plural of accidens, which would normally take the

form 'accidentes,' but if declined as a neuter i-stem noun could take the form 'accidentia.' It

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is in this sense that the word "accidentibus" (first paragraph) is read as dative plural of

'accidens' ('accident'), and "accidentia" (second paragraph) is read as its nominative plural.

By the same token, "accidentalibus concurrentibus" (first paragraph) is read as dative plural

of 'accidentale concurrens' ('accidental occurrence'), and "accidentalia concurrentia"

(second paragraph) is read as its nominative plural.221

As for the term proprietas (nom. pl.: proprietates), it can stand for both 'property'

(in its Aristotelian sense), and 'propriety' (in its use as a term that describes attributes of

ligatures in early mensural notation). Renner translates the term as "stem" (1980, 8), and in

his commentary argues against a direct reference to 'propriety' in terms of ligature

interpretation (1980, 9). He particularly challenges Vecchi's identification of a passage in

Franco de Colonia's Ars cantus mensurabilis (Marchettus mentioned Franco in his text

without providing a specific citation or quotation—Pomerium, tr. 1, ch. 2; Vecchi 1961, 49,

213)—cf. (Renner 1980, 29). According to Vecchi, the passage should be identified as the

section where Franco discusses ligatures 'cum proprietate' and 'sine proprietate' (CS 1:

125; Reaney and Gilles 1974, 50). Renner, however, interprets Marchettus's text as a

reference to another passage (CS 1: 119; Reaney and Gilles 1974, 30) where the subject

matter is the shape of notes, and more specifically the use of stems (i.e., caudae, tails).

Renner's arguments, and his debatable translation, seem to arise from an attempt to narrow

down the meaning of proprietas, producing a uni-intelligible translation, and resulting in a

221 In his work, Ralph C. Renner (1980, 7–8) translates these terms as "accessories" or "accessory

elements," which unfortunately conceals the link with the Aristotelian concepts.

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failure to acknowledge its multifaceted meanings—i.e., through a construction that could

allow pluri-intelligibility. Especially in a treatise like the Pomerium, where the musical and

philosophical backgrounds coexist so distinctively, these meanings include the

understanding of proprietas not only as an attribute applied to caudae as well as to any

other stem-like signs, or as a reference to the 'propriety' that defines the proper

understanding of ligatures, but most importantly as a reference to the Aristotelian concept or

'property.'222

The presence of philosophical terminology and concepts in Marchettus's work was

not only a trend of his time, but a tradition that he followed from within his Paduan

environment.223 In her paper "The Influence of Aristotle's Philosophy of Nature on the

Pomerium of Marchetto of Padua" (1998), Eleonora Beck has called attention to

Marchettus's particular appropriation of Aristotelian concepts not only to help explaining

many of the features of measured music (via concepts of 'nature,' 'art,' and 'accident'), but

222 The philosophical term 'property' (from 'proprietas') is also rendered under the Latin term

'proprium,' as a direct translation of the Greek '«*4@< '—cf. (Aristotle Top., 1.5.102a–b). In his

translation, Renner consistently fails to render (or at least acknowledge) words according to their appropriate

philosophical terminology, thus concealing the tradition upon which Marchettus wrote his Pomerium—cf.

(Beck 1998).

223 In fact, the Aristotelian influence on medieval scholasticism was especially strong in the

fourteenth century, but it had been brought into prominence already from the time and through the works of

St. Thomas Aquinas (ca. 1224/5–1274), who expanded on interpretations of Aristotle's concepts passed

down through a long line of works by several commentators, at least since the ninth century—al-Farabi

(ca. 872–950), Avicenna (980–1037), Averroes (ca. 1126–1198), and Aquinas's own professor Albertus

Magnus (ca. 1206–1280). In the case of Marchettus's Pomerium, a foundation based on medieval

scholasticism was established through the influence of Syphans of Ferrara, who helped with the

philosophical (predominantly Aristotelian) background and organization of the treatise, as Marchettus

himself declared in his introductory Epistola.

306

also to inform the shape and composition of the treatise itself (via analogy with the 'four

causes': material, formal, effective, and final)—cf. (Marchettus 1318/19, bk. 1, pt. 1;

GS 3: 121; Vecchi 1961, 31).224

In terms of this philosophical approach, the modern musico-technical concept of

'accidental' can account only to a partial meaning and understanding derived from its

medieval philosophical counterpart. An 'accident' is generically defined as something that

differs from 'essence,' or from the 'substance' of the object to which it refers.225 An

'accident' is also purely 'incidental,' and although it may help to define an 'individual,' if it is

omitted (taken away, or disregarded) it will not change the 'essence' of the thing, nor its

recognition. Thus, the musical, modern concept of 'accidental' does not correspond

completely to the philosophical meaning of 'accident,' and therefore 'accidental' cannot be

used indiscriminatingly for 'ficta-signs.' While an 'accidental' may sometimes occur

224 According to Eleonora Beck's insightful analysis, the four causes are also used as means of

justifying (rather than impartially explaining) some of the divisions of measured music, at least with regard

to difference and/or sameness between semibreves. Unfortunately, probably due to the necessary limitations

inherent to a paper, Eleonora Beck did not find time to properly acknowledge Marchettus's explicit use of

the concept of 'accident.'

225 In English renditions of Aristotle's works, the words for 'essence' and 'substance' (derived from

the Latin readings 'essentia' and 'substantia') are often used interchangeably, although in a more specific

discussion only a qualified term such as 'necessary essence' could be equated with 'substance' in Aristotelian

terms. In the Middle Ages, however, the differentiation between the two becomes even less evident in some

authors such as St. Augustine, who also uses both terms interchangeably. It is only with St. Thomas

Aquinas that a differentiation is provided, although the concepts are different than those used by Aristotle.

In adapting and re-interpreting Aristotelian premises according to Catholic doctrine, Aquinas defines that

'substance' is that 'essence' which has been endowed with 'existence,' so to differentiate the material world

from the spiritual one, and to come to the conclusion that it is only in God (as the supreme endower,

creator of things) that 'essence' and 'existence' are one and the same.

307

incidentally in the course of a modern piece, it does alter the 'essence' of the thing to which it

refers (in this case, the pitch or absolute sound), and denotes an 'entity' completely

differentiated from the original 'essence without the accidental.' That is, a pitch such as c

may be defined by having both -ness and sharpness, and if either of these attributes are

omitted, it will cease to be a c . A c-mi, however, may not be understood under the same

parameters of pitch (i.e., absoluteness of sound), but as a purveyor of relations with other

steps. In this case, c-mi may be identified (if viewed from the perspective of the

ficta-gamut) as a step that is mi relatively to a-ut, and (if viewed from a recta-only

perspective) as a c-sol-fa-ut whose solmization syllable has been 'accidentally' (or,

incidentally) changed to mi, and thus pertains to a hexachord other than the three basic ones

(in which c-sol-fa-ut is a commonplace). There are at least two reasons why, in medieval

terms, the 'absolute sound' is not relevant to the 'essence' of any 'step' (generically speaking),

or of a 'c-step' (particularly speaking). First, because it does not help to establish the

relation with the other steps, and it is this relation that is more relevant both to medieval

practice and to medieval theory.226 Second, because the deviation (which the new syllable

creates in terms of a new hexachord, and consequently new relations with the other steps) is

thought of as something that lies outside the standard patterns (the recta-gamut), whether or

226 In modern acceptio, the relation between 'pitches' is essential mostly for practical purposes of

solfeging. In medieval acceptio, however, the relation between 'steps' lies at the core of step-denomination

(litterae), as well as of step-recognition (voces). In this respect, musica-speculativa purposes may be

represented by step-denomination (litterae) obtained through successive calculations of string-lengths (as in

theoretical considerations based on the monochord), whereas practica purposes may be represented by

step-recognition (or deduction) through solmization syllables (voces). Both processes depend on the relation

(intervals) with preceding steps, or may serve in the determination of succeeding ones.

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not the actual sound is changed. For example, the ficta g-fa in the -hexachord sounds the

same as the recta (standard) g-sol-re-ut, whereas the ficta g-mi of the -hexachord will have

a different sound, but both ficta-steps will be thought of as being 'essentially' (not only

'accidentally') different from any recta-step. In other words, the -ness by which c-mi may

be defined is not a 'property' of pitch or absolute sound, but a 'property' of its relations with

the other steps, as much as its mi-ness. In practical terms, in the case of c-sol-fa-ut, that

-ness is in fact a different 'property,' defined by a different relation: it always finds a tone

above itself, and below, it will find either a semitone (when it is a fa) or a tone (when it is a

sol).

In order to illustrate this assessment, let us take a modern example such as a c

raised by a quarter-tone. While late 20th-century musicians may be used to working with

this kind of micro-alteration, conceiving it as a standard event, the same may not be true for

other musicians who either do not work with the micro-tonal universe, or else have not even

been trained in it. These latter will not only consider that the indication

'c -quarter-tone-higher' is an incidental occurrence that has no correspondence within the

standardly accepted (i.e., classical) patterns, but will also find hindrances to visualize

(notate), perceive (aurally), understand (conceptually), and perform. In certain cases, some

of them may even consider that the exactness of intonation is irrelevant, and that the

indication 'quarter-tone-higher' is meant as 'slightly sharpened out of tune.' These kinds of

understanding, which pose all the aforementioned hindrances, arise from the fact that the

c -quarter-tone-higher is not included within the standard classical system of only twelve

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pitches per octave, in which modern musicians are generally instructed. Likewise, the same

hindrances may have arisen for early musicians with regard to a ficta-step such as c-mi,

since it does not pertain to the standard recta-gamut. Thus, only steps such as the ficta

c-mi, or the pitch c -quarter-tone-higher, can be properly called 'accidents' or 'accidental

occurrences' in accordance with the prevailing Aristotelian concept followed during the

Middle Ages and Renaissance.227 Once again, it becomes evident that the current musical

usage and understanding of the term 'accidental,' denoting modern flats ( ) and sharps ( )

and their exactness, cannot be equated to what has been thus far called 'ficta-signs,' which

include the fa-signs ( ) as well as mi-signs ( , or ).

227 In his article entitled "Is Mode Real?," Harold Powers has interpreted differently the

Aristotelian notions of "essence" and "accidence," in their application to discussions about musica ficta.

The essential property of the system is the double nomenclature of Latin letter (littera) and

hexachordal syllable (vox). The letters represents the total collection available to musica recta, and

all the potential „real“ musical relationships within it. (The „accidental“ sharps and flats of musica

ficta have no effect on the „substantive“ relationships of musica recta: the distinction of

„accidence“ from „substance“, originating in Aristotelian metaphysics, is fundamental.)

(Powers 1992, 15)

From Powers's perspective, in fact, it is the litterae that are "essential" or "substantive," while the

voces (syllables) would be only "accidental" or "non-substantive" (perhaps he could even say 'adjectival').

But this seems to contradict his own assessment about the "essential property of the system." Again, it is

to be noted that the voces are as essential to this system as the litterae, for each step of the system is at

once composed, represented, and designated by the conjunction littera-voces (i.e., letter-syllables). In other

words, they are undissociable at least where step-designation, understanding of the system, and even

solmization are concerned. If one vox is changed, then the whole step will also change—not necessarily in

terms of a modern frequency-bias, but conceptually.

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(iii) Particular Terminology: Other Terms Versus Ficta-signs

Having discussed the problematic adoption of the term 'accidentals' for 'ficta-signs,'

there remain four alternatives that need to be considered: 'hexachord-signs,' 'syllable-signs,'

'interval-signs,' and 'solmization-signs.' In the Middle Ages and the Renaissance, adjectival

references to the signs were either based on their shape (i.e., b rotundum, and b quadratum

or quadrum), or, alternatively, based on their alleged aural quality (i.e., b molle, and b

durum).228 The signs themselves served as referents and heralds both of those hexachords

228 When referring to music, the terms molle and durum were initially used to describe qualities of

sound and its production (thus aural qualities), clearly including social and moral connotations. These terms

are apparently related to several other terms used in Greek philosophical tradition, and can be said as derived

(among others) from the Greek words 'malakos [i.e., soft] and 'skleros' [i.e., hard], as defined by

Aristotle—cf. TGL and TLL. In his Meteorologica, he uses these terms as 'qualities of bodies,' and states:

Those things are absolutely hard and soft which satisfy the definition absolutely, and those things

are relatively so which do so compared with another thing. Now relatively to one another hard or

soft are indefinable, because it is a matter of degree, but since all the objects of sense are

determined by reference to the faculty of sense it is clearly the relation to touch which determines

that which is hard and soft absolutely, and touch is that which we use as a standard or mean. So

we call that which exceeds it hard and that which falls short of it soft.

(Aristotle Meteor., 4.4.382a; [trans.] Webster 1923; cf. Lee 1952, 310–315)

Aristotle makes it clear that "touch" is just a term used to define some accepted "standard or mean."

In this sense, the term easily lends itself to further interpretation, and could be used as 'sound,' which entails

both 'audition' (as a practical standard) and 'calculation' (as a speculative mean). Moreover, given that

"relatively to one another hard or soft are indefinable," the use of these terms in a musical context seems

appropriate, for the two varieties of b (according to the Pseudo-Odonian alphabetical denomination for steps)

are clearly differentiated in their sound. Thus, b-molle and b-durum are defined not in relation to

themselves (i.e., to one another), but in relation to other surrounding steps. With respect to the terms

rotundum and quadratum (or quadrum), before they were applied to the two varieties of the letter b, their

application in a musical context had included philosophico-scientific descriptions. For example, they were

used to denote geometrical figures used for calculating or demonstrating proportions (notedly in the case of

quadratum), or to explain models of physical occurrences as in waves of sound (notedly through rotundum),

311

that included them, and their hexachordal families.229 In accordance with this usage, since

the signs served mainly as markings for a hexachord, the generic term 'hexachord-signs'

would seem to be a likely alternative in lieu of 'ficta-signs.' However, this term poses a

problem for the understanding of solmization with regard to pieces that existed before the

advent of a theory of hexachords, or at least before its initial proposition (with Guido

d'Arezzo). This problem would happen, for instance, when trying to understand the scope

(conceptual and practical) of vitium and absonia (i.e., musica ficta) as transmitted and

defined in the anonymous treatise Scolica enchiriadis.

Another alternative, that would seem to circumvent the restrictions imposed by the

previous option, might be found in the term 'syllable-signs.' However, this would also be

too restrictive, for the term associates music-reading to a specific kind of solmization purely

based on syllables. It is true that the term 'syllable-signs' has the double advantage of

or even to describe faster and variegated rhythmic motion-patterns (by attributing roundness to them, as

opposed to the fullness of slower ones), etc. For a small sample of early musical usage of all of these

terms (or derivatives and related terms)—calling forth, by means of their sensible attributes (tactile, aural,

and geometrical), connotations of social ethics and morality as well as rhetorical purposes—cf. (Capella a.

439, bk. 9; Meibom 1652, 2: 180, 187, 191; Dick 1925, 496, 511–512, 518–519; [trans.] Stahl et al.

1971–1977, 361, 369–370, 374); (Boethius a. 510, bk. 1, chs. 1, 14, and 21; GB-Ctc ff. 5v–7r, 15v, 21v;

PL 63: 1168–1170, 1179, 1188, Friedlein 1867, 180–184, 200, 212–213; [trans.] Bower 1989, 2–5, 21,

39–41); (Isidorus ca. 627–636, bk. 3, ch. 20; GS 1: 22; PL 82: 164–166; Lindsay 1911, 1: ff. K7r–K8r;

[trans.] SR 1950, 95–96; SR 1998, 151–152). Naturally, as references to hexachords, these

terms—descriptive of b-attributes—were employed only after Guido's propositions came into acceptance.

For some presentations on these terms, their Greek and philosophical background, and their use in later

musical theory, cf. the articles by Mountford (1920, esp. 17–28), Dahlhaus (1955), and more recently the

entry authored by Michael Beiche and published in 1995 in the Handwörterbuch der musikalischen

Terminologie (HmT, s.v. 'Dur — moll,' esp. 1–6).

229 Hexachords such as - and -hexachord, which include either or , were said to belong to

the molle family, while those such as - and -hexachord, which include either or , were said to belong

to the durum family.

312

making it clear that one such sign as stands for fa, or that (or ) stands for mi, and of

denoting, by necessity an underlying intervallic relationship with other steps and their

syllables. But, it preserves the disadvantage of limiting the understanding of signs to a

paradigm that is not only based on syllabic solmization, but also one that suggests different

syllables for different steps (according to the Guidonian paradigm), which was not entirely

true of all syllabic-solmization propositions—e.g., noeanne/noeagis solmization. In other

words, other kinds of solmization—especially those that were not based on syllables—

would be suggestively discarded where the notion of a 'syllable-sign' was applied. For

example, in the case of solmizing by means of pure and simple step-letters (whether or not

of the Pseudo-Odonian kind), the absolute (frequency-defined) sound was not the aim of

solmization, but the proper relation (intervals) between step-letters, as argued above. Even if

the Guidonian paradigm is accepted as predominant during the Middle Ages and Renais-

sance, different solmization systems (tetrachordal, hexachordal, or others) may have been

used (extensively or not), or alternatively devised or chosen (whether or not by an individual

performer's will), and must not be discarded by any generic term being artificially

established in this work.230

A third alternative could be the term 'interval-signs,' for the signs indicate not only

attributes of the specific steps, but mainly specific kinds of interval to adjacent and

nonadjacent steps—a semitone below and whole tone above for the fa-sign ( ), and a

230 Cf. chapters 1 and 2 for considerations about other systems, pre- and post-Guido's

propositions on hexachordal solmization, its acceptance and later predominance, as well as evidences of

other kinds of solmization, apparently resistant to the Guidonian paradigm.

313

semitone above and whole tone below for the mi-sign ( or )—whether in the same

hexachord, tetrachord, or other structures. Nevertheless, 'interval-signs' might lead to the

mistaken understanding that signs were meant only as alterations of surrounding intervals,

perhaps indicating a sound-stability (pitch) of the specific steps to which they are attached;

or in other words, changing the sound (pitch) of the surrounding steps while preserving the

sound (pitch) of the attached step, in order to obtain the required intervallic alteration. For

instance, if a was notated at the place of g (making it a g-fa), it could be interpreted not as

an inflection on the sound of the g, but as an alteration on the interval with its surrounding

steps (f and a). By means of this interpretation, the g would maintain the same sound as a

regular g-sol-re-ut, but f (now solmized as f-mi) would be the one step to suffer a sound

alteration, making it equivalent to f .231 If it is true that a sign may have been used

(paradoxically and ironically) to alter the interval between the step to which it was attached

and others, without changing the sound of the step itself, then this kind of use may as well

have been restricted, due to a particular composer's intention or taste, patron, city, region, or

perhaps even to the context or design of a particular composition.232 In any event, whether

231 Such an understanding was offered by Andrew Hughes in analyzing relevant passages in

Ugolino's Declaratio musicae disciplinae (ca. 1430–35), and later corroborated by Margaret Bent in "Musica

Recta and Musica Ficta," where her interpretations were based on evidence presented in the treatises by the

anonymous Parisian author of the Berkeley manuscript (Anon. Berkeley 1375) and as well as those by

Ugolino—cf. (Hughes 1969; 1972: 29–30, 37–38, 44–45, 51; Bent 1972, 85–89). The idea, was criticized

by Karol Berger in his famous work on ficta.—cf. (K.Berger 1987, 17–18).

232 The latter interpretation has been speculatively suggested by Seay (1969) as a solution for

reading the signs in Lorenzo Masini's L'Antefana, but that would be possible only if the 'permutation'

instances in that work were ignored.

314

this interpretation of signs can be truly verified or not, it ought to be considered an

exception, rather than a widespread practice and understanding. So, the term 'interval-signs'

must be dismissed, together with the others.

Still another term, that could more easily comply with all that has been said and

defined so far, would be 'solmization-signs.' It has the apparent advantage of not being

dependent on specific solmization systems, but allowing diverse possibilities and/or choices.

Furthermore, it clearly states the most basic purpose of signs, that is, to serve solmization.

Notice that in order for this term to be effective, the term 'solmization' per se must be

generalized to mean 'reading early music' from any kind of early notation. However, this

generalization can generate some misapprehensions regarding origin and usage. For

instance, when describing J. Leodiensis's definition for 'false mutation,' Andrew Hughes has

suggested that the term 'solmization' may have been derived from the syllables sol and mi.

He [Jacobus Leodiensis] called mutation between the standard [recta] and the new [ficta] hexachords

false mutation, and that which it produced falsa musica (CS, ii, p.239a). Mutation of this kind

placed adjacent the syllables sol and mi , from which Renaissance theorists abstracted the term

'solmization': medieval writers used only the noun 'solfatio' and verb 'solfare.'

(NG 1, 17: 461, s.v. 'Solmization'; NG 2e, s.v. 'Solmization,' § I.4)

[Interpolations mine]

In fact, research indicates that not only the immediate Latin equivalents for the

anglicized 'solmization' (from 'solmizatio' and 'solmisatio'), but all its closest spellings

(whether as nouns, or verbs and adjectives) seem to have gained currency only in the

Renaissance. An inspection of a sample of Latin treatises revealed that only 33 (involving

30 authors) employed equivalents to 'solmization' in various Latin spellings and

315

derivations.233 Even so, 26 of those treatises (involving 24 authors) were written during the

Renaissance. Among the several Latin spellings one may find the following: (nouns)

solfatio, solfa, solfatoria, solfisatio, solfizatio, solmisatio, solmizatio, solmifatio, solfatura;

(verb) solfare, solfiare, solfaciere, solfisare, solfizare, solmisare; (verbal adjectives)

solfizans, solmisans, solmizans; and also the noun solmisator (a designation apparently

given only by Martin Agricola [1539, ch. 2, f. Biijr], and, with the spelling solmizator, by

Joachimus Wolterstorpius [1530's/1550's, ch. 2; Kast 1963, 25–26]—the latter probably

based his brief treatise on Agricola's, for several passages are verbatim with his Rudimenta

musices). Naturally, many treatises (irrespective of their dates) used different spellings

indiscriminately, but as stated by Hughes in the thirteenth and fourteenth centuries the most

common forms were the noun solfatio, and the verb solfare—although solfiare and

solfaciere also seem to be have been used exclusively in that period. On the other hand,

closely related spellings like solfisatio or solfizatio, and solfisare or solfizare seem to have

been used for presentations in Renaissance treatises.234

233 The present research on the term 'solmization' was realized via the search engine of TML,

which included 673 treatises at the time this inspection on 'solmization' and derivatives—TML currently

holds transcription of over 800 treatises.

234 In the chronological list of treatises given below, the ones preceded by an asterisk (* ) indicate

use of spellings with the morpheme 'solmi,' instead of 'solfa' or 'solfi '—there are only 11 treatises thus

marked. Notice that nearly all of those treatises were written near the end of the fifteenth century, except for

the one written by the anonymous Carthusian monk (here dated ca. 1400), which cannot be dated earlier

than mid fourteenth century (since it makes reference to Tewkesbury's Quatuor principalia), but also,

according to Coussemaker, may have been produced early in the 15th century, based on the history of the

manuscript B-Gu 70(71) (olim 421), ff. 124r–159v, Ghent, 1503–4, edited by Coussemaker (CS 2:

434–483)—cf. also (CS 2: xxii–xxvii; Grove 6, 1: 443; Aluas 1996, 1: 189–197). It is also possible,

since that copy of the treatise was made in 1504, that the introduction of the term is due to a later scribal

316

If Hughes's interpretation is correct (that the term 'solmization' alludes to a

ficta-mutation involving the syllables sol and mi), then the original terms 'solfatio' and

'solfare' (and all others based on the morpheme 'solfa' or 'solfi') would stand for a mutation

involving the syllables sol and fa). Such a mutation would be considered 'irregular,' not

only because it would involve two syllables from the same hexachordal subset, but also

because it would necessarily involve a mutation between two nonadjacent hexachords (i.e.,

choice—the term occurs only twice in the treatise, in the same paragraph, through the verb solmizare. The

chronological list is as follows: (13th century [4 authors, 4 treatises]) — (Zamorensis, 1260/80, ch. 5;

GS 2: 378; Robert-Tissot 1974, 62); (Elias Salomon 1272, chs. 2, 20; GS 3: 18, 42); (Amerus 1271;

Ruini 1977, 32, 96); (Villa-Dei(?) ?13th cent.; Seay 1977a, 18); (14th century [2 authors, 3 treatises])

— (Engelbertus Admontensis a. 1320, tr. 3, ch. 4; GS 2: 322); (Leodiensis in. 13th cent., chs. 5, 8; Smits

van Waesberghe, et al. 1988, 110, 114); (Leodiensis p. 1330, bk. 6, chs. 61, 63–64, 65, 67, 69, 101; CS

2: 280, 285–288, 291, 294, 301, 360; Bragard 1955–73, 6: 162, 173–178, 183, 188, 199, 286); (15th

century [10 authors, 11 treatises]) — * (Anon. Carthus. ca. 1400, pt. 1, ch. 8; CS 2: 449); (Olomons

1404/9, ch. [6]; Seay 1977c, 19); (Person 1417, ch. 3; Müller 1907, 184); (Anon. 11 med. 15th cent.; CS

3: 417, 419, 421–422, 445, 467; Wingell 1973 1: 4, 10, 16–17, 86, 152); (Tallanderius med. 15th cent.,

Seay 1977d, 4, 11); (Tinctoris p. 1477, ch. 7; CS 4: 13; Seay 1975–78, 2: 52); (Guillelmus mon. ca.

1480–90, ch. 5; Seay 1965, 32); (Ramos de Pareja 1482, pt. 1, tr. 2, ch. 7; f. [17v]; Wolf 1901, 44; Terni

1983, 2: 102); (Bonaventura da Brescia 1489, ch. 16; Seay 1980, 47); (Tinctoris 1495, f. b iiiiv, s.v.

'solfisatio'; CS 4: 188; Machabey 1951, 53; Parrish 1963, 60); (Zalka 1490; Bartha 1934, 68–69,

117–118); (16th century [15 authors, 16 treatises]) — * (Anon. Introd.mus. ca. 1500; Riemann 1897,

157, 158); (Cochlaeus 1511–14, tr. 2, ch. 3, 6, ff. Biiiv, Biiiiv); * (Felstin 1517, chs. [Preface], 2, 3 , ff.

Aijv, Aviv–Biv, Bijr, Biijv–Cir, Cijr, Ciijr, Div, Diijr–iiij r); * (Rhau 1517, chs. 3, 4, 7, 8, ff. Ciijr–v,

Djr–ijr, Dviijv, Ejr); (Rossetti 1529, ch. 4; Seay 1981, 14); * (Wolterstorpius 1530's/1550's, ch. 2; Kast

1963, 25–26); (Vanneo 1533, bk. 1, ch. 13, f. 12r); * (Saess p. 1536, chs. [dedicatoria], 2, 5;

Federhofer-Königs 1964, 64, 71, 74, 76); * (Agricola 1539, chs. Preface, 2, 3, ff. Avir–vijv, Biv, Biij r–viv,

Bvijr); * (Heyden 1540, bk. 1, chs. Index, 1, 2, 4, 6, 8, ff. A6v, 2, 10, 13, 18–20, 24–25, 42, 54);

* (Vogelsang 1542, chs. [Index], 1, 4; Federhofer-Königs 1965, 78, 79, 84); * (Glarean 1547, bk. 3, ch. 11,

220); * (Coclico 1552, pt. 1, f. B ijr); * (Finck 1556, ff. Aiijv, Fijr, Ni r, Ssiiijr); (Stoquerus ca. 1570, chs.

1, 2, 3, 5, 18; Rotola 1988, 102, 104, 108, 112, 114, 120, 190); (Stoquerus p. 1570, ff. 41r, 42v).

To this list, one could append the Summa musice, considering the differences between its two

available editions (Gerbert's and Page's). Gerbert gives one occurrence of the word "solfamus" (2nd. person

pl. pres. ind. act. of 'solfo, -are'), but Page reads it to "solvamus" (2nd. person pl. pres. subj. act. of 'solvo,

-ere,' which has many meanings depending on the context, but can be loosely translated into 'to release; to

solve; to set free'). Although Page does not mention Gerbert's reading, the context of the passage seems to

warrant Page's reading—cf. (Perseus and Petrus ca. 1200, ch. 25; GS 3: 245; Page 1991, 208).

317

separated by two fifths relatively to a circle of fifths).235 In other words, if this was a

recta-mutation (however 'irregular'), then it would necessarily involve the nonadjacent

hexachords based on and . There are only two steps in the entire recta-gamut that could

support such a mutation: c-sol-fa-ut and its upper octave cc-sol-fa —or in modern

pitch-notation, equivalent to c' and c". In the case of the term 'solmization' (as seen above),

a hexachordal change between sol and mi on the same step-letter would necessarily denote a

'mutation' of the 'ficta'-species, or could alternatively denote a 'permutation.' The hexachords

solmized in this hypothetical sol=mi mutation would be separated by three consecutive

fifths (relatively to a circle of fifths), and in a sol/mi permutation, the hexachords would be

separated by five fifths (and additionally, as in any permutation, the step-sounds would be

necessarily different). In both situations, there would always be at least one ficta-hexachord

involved in the process of change, although such a distance between hexachords would

impose solutions that are not commonly found in the repertoire—cf. TABLE II , p. 191, in

order to visualize these hexachords and the distance between them relatively to a circle of

fifths.

Although no treatise consulted has provided evidence of Hughes's interpretation, or

any of the assessments above for the origin of the term 'solmization,' its possibility is

235 Leodiensis's definitions for 'irregular mutation' (irregularis mutatio) are provided in his

Speculum musicum, together with definitions of 'false mutation' (falsa mutatio), whose meanings are

briefly surveyed in chapter 4 together with other considerations (esp. p. 165–170). Although these kinds of

mutation ultimately denote different concepts, in his explanations the latter can be interpreted as a particular

case of the former, but certainly not the opposite—cf. (Leodiensis p. 1330, bk. 6, chs. 63, 66; CS 2: 285,

293–294; Bragard 1955–73, 6: 172–173, 185–187).

318

certainly admissible. The term 'solmization-signs' would then imply, through its own

morpheme ('solmi'), the use of musica ficta as a resource for 'reading early notated music,'

and would, therefore, be fairly appropriate for the purposes of the present work. However,

one might argue that due to its late adoption in historical treatises, the term 'solmization'

should not be considered, since it may be misleading; that is, since it is rather a Renaissance

term, purists could argue that it pertains neither to medieval musical practices, nor to

non-Guidonian hexachord-based readings. As a counter-argument, it may be considered

that also the term musica ficta is a late one, although modern scholarship has chosen to

adopt it, based not only on late medieval discussions and suggestions toward an appropriate

substitute for musica falsa and vitium, but also in its more definite adoption by some

Renaissance auctoritates. In any case, if all these concepts behind the terms 'solmization'

and 'musica ficta' are properly and consciously unveiled, them their modern usage cannot be

seen as misleading. There is, however, one only and strong reason not to adopt

'solmization-signs' and, instead, favor 'ficta-signs.' Historical treatises do provide clear

statements that although the signs of and served solmization, they were ultimately

described and identified as 'signs of musica ficta' (i.e., signa falsae musicae, or signa fictae

musicae, or signa coniunctae).236

236 In the quotation from Anonymous 11, below, there is no explanation why Wingell chose the

translation "signified" for the word "signata" given explicitly in the first phrase, and "signed" for the same

"signata" implied in the second phrase. It is clear in the text that the verb 'signo, -are' is meant as 'to sign,'

and not as 'to signify.'

319

Falsa musica dicitur esse quando locatur

molle vel quadrum in loco non usitato.

Sunt enim duo signa falsae musicae,

scilicet, molle et quadratum. Ubi ponitur

rotundum dicitur fa; ubi vero quadrum

dicetur mi. Et sic potest unam speciem in

aliam transmutari, ut visum est in capitulo

de proportionibus.

(Anon. 2 ?ex. 13th cent.; CS 1: 312 ; Seay

1978, 32)

False music is said to exist when

molle or quadrum is placed at a point

where it is not customary.

Indeed, two are the signs of false music,

namely, molle and quadratum. Where

rotundum is placed, [the syllable] fa is said;

however, where quadrum [is placed], [the

syllable] mi will be said. And thus one

species [of interval] can be transmuted into

another, as it was seen in the chapter on

proportions [of intervals].

(my translation; cf. Seay 1978, 33)

————————

Igitur scire debes, sicut dictum est, <quod>

duo sunt signa falsae musicae, scilicet b

rotundum et ista alia figura <quadratum>.

Et talem proprietatem habent, videlicet quod

b rotundum habet facere de semitonio

tonum, tamen in descendendo, et de <tono>

in ascendendo habet facere <semitonium>.

Et e converso fit de alia figura ista , scilicet

quod de tono descendente habet facere

semitonium, et de semitonio ascendente

habet facere tonum. Tamen, in illis locis ubi

ista signa requiruntur, <sunt>, ut superius

dictum est, non falsa sed vera et necessaria.

(Pseudo-de Vitry ca. 1322, ch. [14]; Reaney,

et al. 1964, 22–23; I-Rvat Barberini 307,

f.19r; CS 3: 18)

Therefore, you ought to know, as has been

indicated, that musica falsa has two signs,

namely the round and that other figure .

And they have such a property as, in the case

of round , to make of a descending semitone

a tone, and of an ascending tone, a semitone.

And that other figure , effects the reverse;

that is, of a descending tone it makes a

semitone, and of an ascending semitone, a

tone. Nevertheless, in those places where

these signs are required, they are, as has been

indicated above, not false, but true and

necessary.

(Plantinga 1961, 213)

————————

[C]oniuncta est alicuius proprietatis seu

deduccionis de loco proprio ad alienum

locum secundum sub vel supra intellectualis

transposicio. Pro cuius evidencia notandum

est, quod omnis coniuncta aut signatur per b

aut # in locis inusitatis positum.

(Anon. Berkeley 1375, tr. 1, ch. 3;

Ellsworth 1984, 50, 52)

[C]oniuncta is the mental transposition of

any property or hexachord from its own

location to another location above or below.

As evidence of this, it must be noted that

every coniuncta is signed by b or #, placed

in an unusual location.

(Ellsworth 1984, 51, 53)

320

————————

Signa autem ut hic considerantur hanc fictam

musicam demonstrativa sunt B molle sive

rotundum, cui haec vox fa dicitur deservire,

et quadrum sive durum, cui haec vox mi

penitus famulatur, [...].

(Ugolino ca. 1430–1435, bk. 2, ch. 34;

Seay 1959–62, 2: 46; Hughes 1972, 22)

The signs designed to display musica ficta

are , to which we immediately utter the

subservient syllable fa, and , to which we

pronounce mi, [...].

(Hughes 1972, 30)

————————

Et sciendum quod omnis coniuncta signata

per b molle dicitur fa; sed per b quadratum

dicitur mi, loco cuius frequenter h. Quum

ergo cognicio talium coniunctarum

necessaria sit in cantu plano, et eciam

organico, idcirco videndum diligenter est de

eis et scrutandum.

(Anon. 11 ?med. 15th cent., ch. [2];

Wingell1973, 28–29; CS 3: 426)

One should know that every coniuncta

signified by soft B is sung as fa, but if

signed by square B, in place of which an h

frequently appears, it is sung as mi. Since,

then, the knowledge of these coniunctae is

necessary in plain chant and also polyphony

(organum), therefore, coniunctae must be

diligently considered and studied.

(Wingell 1973, 203)

————————

Duo sunt signa coniunctarum, scilicet

quadrum, quod coniunctam fieri demonstrat

in locis b mollaribus. Et b molle, quod in

locis duralibus eam indicat. enim

quadrum mi, orbiculare fa notat, quippe fa

ευφονιαµ [euphonian], mi vero

κακοφατοµ [kakophaton] sanat.

(Rhau 1517, ch. 7, f. [D viijv])

Two are the signs of the coniunctae, namely

quadrum [i.e., square b], which shows the

coniuncta to be made in the place of the

mollare [i.e., soft b, same as molle], and

the molle , which indicates it [the

coniuncta] in the place of the b durale [i.e.,

hard b, same as durum]. Indeed, the

quadrum denotes mi , [and] the orbicularis

[i.e., orbicular, same as rotundum] denotes

fa, for in fact fa heals euphony, while mi

heals the cacemphaton.

(my translation; cf. K.Berger 1987, 116)

I believe that enforcing the term ficta-signs as a terminological standard has

enhanced the clarity and rigor of my own analyses of musical and theoretical texts.

321

Whether or not my commitment to this and other usages specific to this dissertation find

their way into the discursive mainstream of ficta scholarship, I hope the particular

perspectives laid out in this study serve to promote further investigation of this fundamental

segment of the musical practices of pre-modern Europe.

322

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Anonymous. Rhetorica ad Herennium. ca. 1st cent. B.C. Source and translation: Caplan1954.

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———, trans. Bartolomeo Ramis de Pareia: Musica practica. Musicological Studies andDocuments, vol. 44. Neuhausen-Stuttgart: Hänssler-Verlag, American Institute ofMusicology, 1993. (See Ramos de Pareja 1482.)

Mocquereau, André, Dom, ed. Les Principaux manuscrits de chant gregórien, ambrosien,mozarabe, gallican: Antophonaire monastique XIIIe siècle, Codex F. 160 de laBibliothèque de la Cathédrale de Worcester. 2 vols. Paléographie Musicale, vol.12. Tournai, Belgium: Desclée et Cie, 1922.

Monachus Carthusiensis. (See Anonymous monachus Carthusiensis.)

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———, ed. Three Medieval Rhetorical Arts. Berkeley: University of California Press,1971.

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Nicolaus de Capua. (See Capuanus, Nicolaus.)

Niecks, Frederick. "The Flat, Sharp, and Natural: A Historical Sketch." Proceedings of theMusical Association, 16th Session (1889–1890), 79–100. Reprint. Vaduz: Kraus,1966.

Odington, Walter. Summa de speculatione musicae. in. 14th century. Sources: CS 1:182–250; Hammond 1970, 42–146. (For translation of Part VI, see Huff 1973.)

Odo. (See Pseudo-Odo.)

Odo d'Arezzo. Tonarius. ex. 10th cent. Sources: GS 1: 247–250; CS 2: 81–109;PL 133: 755–158.

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350

Parr, Roger P., trans. Geoffrey of Vinsauf: Documentum de modo et arte dictandi etversificandi (Instruction in the Method and Art of Speaking and Versifying).Milwaukee, Wis.: Marquette University Press, 1968. (See Vinsauf p. 1213–14.)

Parrish, Carl. The Notation of Medieval Music. New York: W.W. Norton, 1957.

———, trans. Dictionary of Musical Terms by Johannes Tinctoris: An EnglishTranslation of "Terminorum musicae diffinitorium" Together with the Latin Text.London: The Free Press of Glencoe, Collier-Macmillan, 1963. (See Tinctoris1495.)

———. "A Renaissance Music Manual for Choirboys." In Aspects of Medieval andRenaissance Music: A Birthday Offering to Gustave Reese, edited by Jean LaRue,649–664. New York: W.W. Norton, 1966.

Peacham, Henry. The Garden of Eloquence. 2nd. ed. London: H. Iackson, 1593. Reprint.Facsimile. Introduction by William G. Crane. Gainesville, Fl.: Scholars' Facsimilesand Reprints, 1954.

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———. Guido d'Arezzo's Regule rithmice, Prologus in Antiphonarium, and Epistola adMichahelem: A Critical Text and Translation With an Introduction, Annotations,Indices, and New Manuscript Inventories. Ottawa, Canada: The Institute ofMediaeval Music, 1999. (Guido ca. 1027/1032p; ca. 1027/1032r; ca. 1032)

Perseus and Petrus. Summa musice. ca. 1200. Source: GS 3: 190–248; Page 1991,139–211. (For translation, see Page 1991, 45–137.)

Petrus palma ociosa [Petrus frater dictus palma ociosa]. Compendium de discantumensurabili. 1336. Source and translation: Wolf 1913–14: 505–534 [Latin andGerman in facing columns] ([Latin] http://www.music.indiana.edu/tml/14th/PETCOM_TEXT.html).

Philippe de Vitry. (See Pseudo-Vitry.)

Phillips, Nancy Catherine. "Musica and Scolica enchiriadis: The Literary, Theoretical , andMusical Sources." Ph.D. diss., New York University, 1984.

351

Pickard-Cambridge, W.A., trans. "Topica and De Sophisticis elenchis." In The Works ofAristotle, edited by William David Ross, vol. 1. Oxford: Clarendon, 1928. (SeeAristotle Top.)

Pike, Lionel. Hexachords in Late-Renaissance Music. Aldershot, England: Ashgate, 1998.

Pirrotta, Nino, ed. The Music of Fourteenth -Century Italy. Corpus Mensurabilis Musicae,vol. 8, no. 3. S.l.: American Institute of Musicology, 1962.

Plantinga, Leon. "Philippe de Vitry's Ars Nova: A Translation." Journal of Music Theory 5,no. 2 (1961): 204–223.

Powers, Harold. "Is Mode Real?: Pietro Aron, the Octenary System, and Polyphony."Basler Jahrbuch für historische Musikpraxis 16 (1992): 9–52.

Praetorius, Michael. Syntagma Musicum III. Wolffenbüttel: Elias Holwein, 1619. Reprint.Facsimile. Documenta Musicologica, 1st Series, vol. 15. Edited by WilibaldGurlitt. Kassel: Bärenreiter, 1958. (For translation, see Lampl 1957.)

Prosdocimus de Beldemandis. Contrapunctus. 1412–1425/28. Source: CS 3: 193–99;Herlinger 1984, 26–94 [even]. (For translation, see Herlinger 1984, 27–95 [odd].)

———. Parvus tractatulus de modo monocordum dividendi. 1413–25/28. Sources:CS 3: 248–258; Herlinger 1987, 64–116 [even]. (For translation, see Herlinger1987, 65–117 [odd].)

———. Tractatus musicae speculativae contra Marchetto de Padua. 1425. Source:Baralli and Torri 1913, 731–762.

Pseudo-Cicero. Rhetorica ad Herennium. (See Anonymus. Rhetorica ad Herennium.)

Pseudo-de Vitry. Ars nova. ca. 1322. Source: I-Rvat Barberini 307, ff. 17r–20v

(http://www.music.indiana.edu/tml/14th/VITANV_MBAVB307.html); CS 3: 13–22(http://www.music.indiana.edu/tml/14th/VITARSN_TEXT.html); Reaney, et al.1956, 13–32 (http://www.music.indiana.edu/tml/14th/VITARN_TEXT.html);Reaney, et al. 1964, 13–32 (http://www.music.indiana.edu/tml/14th/VITARNO_TEXT.html). (For translation, see Plantinga 1961, 205–220 [English];Reaney, et al. 1957, 12–30 [English]; 1964, 33–51 [French].)

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Pseudo-Franco. Compendium discantus. ?13th century. Sources: GB-Ob 842, ff.60r–62v (http://www.music.indiana.edu/tml/13th/FRACOMO_MOBB842.html);CS 1: 154–155 (http://www.music.indiana.edu/tml/13th/FRACOM_TEXT.html);Reaney 1996, 50–56 (http://www.music.indiana.edu/tml/13th/FRACOMP_TEXT.html).

Pseudo-Johannes de Muris. (See Pseudo-Muris.)

Pseudo-Muris. Ars discantus. med. 14th century. Source: CS 3: 68–113 (http://www.music.indiana.edu/tml/14th/MURARSD_TEXT.html).

Pseudo-Odo. Dialogus de musica. ex. 10th century D. Sources: GS 1: 251–264; PL133: 757–774. (For partial translation, see SR 1950, 103–116; SR 1998, 198–210.)

———. Musica artis disciplina (or De musica). ex. 10th century M. Sources: GS 1:265–284; PL 133: 773–796.

Pseudo-Philippe de Vitry. (See Pseudo-de Vitry.)

Pseudo-Tunstede. (See Tewkesbury, Johannes de.)

Puttenham, George. The Arte of English Poesie. [1589]. Edited by Gladys DoidgeWillcock and Alice Walker. Cambridge: Cambridge University Press, 1936.

Quintilian [Marcus Fabius Quintilianus]. Institutio oratoria. ca. 93/95. Source andtranslation: Russel 2001.

Quintilianus, Aristides. (See Aristides Quintilianus.)

Ramos de Pareja, Bartolomé. Musica practica. Bologna: Baltasar de Hiriberia, 1482.Reprints. Bologna: Forni, 1969. Madrid: Joyas Bibliográficas, 1983 (see Terni1983, vol. 1). Sources: Wolf 1901, 1–112 (http://www.music.indiana.edu/tml/15th/RAMMP1T#_TEXT.html [# = 1, 2, 3]; http://www.music.indiana.edu/tml/15th/RAMMP2_TEXT.html; http://www.music.indiana.edu/tml/15th/RAMMP3T#.html [# = 1, 2]); Terni 1983, 2: 73–148. (For translation, see Terni 1983, 2:151–242 [Spanish]; Miller 1993 [English].)

Randel, Don Michael, ed. The New Harvard Dictionary of Music. Cambridge, Mass.: TheBelknap Press of Harvard University Press, 1986.

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353

Reaney, Gilbert, ed. De musica libellus (MS Paris, Bibl. nat. lat. 6286), anonymus;Tractatus de discantu (MS Saint-Dié, Bibl. municipale, 42), anonymus;Compendium discantus (MS Oxford, Bodl. Libr., Bodley 842), Pseudo-Franco deColonia; Traitié de deschant (MS Paris, Bibl. nat., lat. 15139), anonymus; Traitiéde deschant (MS Paris, Bibl. nat., lat. 14741), anonymus. S.l.: American Instituteof Musicology, 1996. (See Anon. 2 ?13th cent.; Pseudo-Franco ?13th cent.)

Reaney, Gilbert, and André Gilles, eds. Ars cantus mensurabilis <ad> Franconis deColonia. Corpus Scriptorum de Musica, vol. 18. S.l.: American Institute ofMusicology, 1974. (See Franco de Colonia p.p. 1250.)

Reaney, Gilbert, André Gilles, and Jean Maillard, eds. Ars Nova. Corpus Scriptorum deMusica, vol. 8. S.l.: American Institute of Musicology, 1964. Reprinted from aseries of articles originally published in Musica Disciplina: Reaney et al., "The 'ArsNova' of Philippe de Vitry" (vol. 10 [1956]: 5–33); Gilles, "Un Témoignage inéditde l'enseignement de Philippe de Vitry" (vol. 10 [1956]: 35–53); Gilles, et al.,"Philippe de Vitry — Ars Nova (Translation of text)" (vol. 11 [1957]: 12–30);Gilles and Reaney, "A New Source for the Ars nova of Philippe de Vitry" (vol. 12[1958]: 59–66); Reaney, "A Postscript to Philippe de Vitry's Ars Nova" (vol. 14[1960]: 29–31). (See Pseudo-Philippe de Vitry ca. 1322.)

Reckow, Fritz. "Vitium oder Color rhetoricus?: Thesen zur Bedeutung der Modelldiszi-plinen grammatica, rhetorica und poetica für das Musikverständnis." In Text undMusik: Neue Perpektiven der Theorie, edited by Michael Walter. Munich: WilhelmFink, 1992.

Reichenau, Berno of. (See Berno Augiensis.)

Reichenau, Hermannus of. (See Hermannus Contractus.)

Remigius Autissiodorensis. Commentum in Martianum Capellam. 876/883. Sources:GS 1: 63–94; PL 131: 931–964; Lutz 1962–65 [in 2 vols.]; Smith 1987, 99–432.(For translation, see Smith 1987, 99–432.)

Renner, Ralph Clifford. The "Pomerium" of Marchettus of Padua: ATranslation andCritical Commentary. Ph.D. diss., Washington University, Saint Louis, Miss.,1980. (See Marchetto 1318/19.)

Rhau, Georg. Enchiridion utriusque musicae practicae. Wittenberg: Georg Rhaw, 1517.Reprint, 1538. Facsimile. Edited by Hans Albrecht. Kassel: Bärenreiter, 1951.http://www.music.indiana.edu/tml/16th/RHAENC_TEXT.html.

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Roberts, W. Rhys, trans. Rhetorica. Oxford: Clarendon Press, 1924. Reprint. In TheWorks of Aristotle, edited by William David Ross, vol. 11. Oxford: ClarendonPress, 1946, 1951, 1960. (See Aristotle Rhet.)

Rohloff, Ernst, ed. Der Musiktraktat des Johannes de Grocheo. Leipzig: Kommissions-verlag Gebrüder Reinecke, 1943.

Rooley, Anthony. "Renaissance Music and the Emblem Tradition: Its Effect onPerformance Attitudes." In Struttura e retorica nella musica profana delcinquecento: Atti del Convegno Trento, Centro S. Chiara 23 ottobre 1988, editedby Marco Gozzi, 157–189. Rome: Edizioni Torre d'Orfeo, 1990.

Rosenstiel, Léonie, trans. Anonymous (Ninth Century): Music Handbook (MusicaEnchiriadis). Translations, vol. 7. Edited by Albert Seay. Colorado Springs:Colorado College Music Press, 1976. (See Anon. ME a. 900.)

Ross, William David, ed. Aristotelis Topica et Sophistici elenchi. Oxford: Clarendon,1958. (See Aristotle Top.)

———, ed. Ars rhetorica. Oxford: Clarendon Press, 1959. (See Aristotle Rhet.)

———, ed. Aristotelis Physica. Oxford: Clarendon Press, 1960. (See Aristotle Phys.)

Rotola, Albert C., S.J., ed. and trans. Gaspar Stoquerus: De musica verbali libri duo.Greek and Latin Music Theory, vol. 5. Lincoln: University of Nebraska Press,1988. (See Stoquerus ca. 1570)

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Rusconi, Angelo, ed. Guido d'Arezzo monaco pomposiano: Atti dei Convegni distudio—Codigoro (Ferrara), Abbazia di Pomposa, 3 ottobre 1997; Arezzo,Biblioteca Città di Arezzo, 29-30 maggio 1998. Firenze: Leo S. Olschke, 2000.

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Sadie, Stanley, ed. The New Grove Dictionary of Music and Musicians, 20 vols. 1st. ed.London and New York: Macmillan, and Grove's Dictionaries of Music, 1980.

Sadie, Stanley, and John Tyrrell, eds. The New Grove Dictionary of Music and Musicians,29 vols. 2nd. ed. London and New York: Macmillan; Grove's Dictionaries ofMusic, 2001. (See Macy 2001.)

Saess, Heinrich. Musica plana atque mensurabilis una cum nonnullis solmisationisregulis certissimis insertis summa diligentia compendiose exarata. p. 1536.Source: Federhofer-Königs 1964, 64–94.

Salomo, Elias. Scientia artis musicae. 1274. Source: GS 3: 16–64 (based on I-Ma D.75).

Santosuosso, Alma Colk, ed. Paris, Bibliothèque nationale, fonds latin 7211: Analysis,Inventory, and Text. Publications of Mediaeval Musical Manuscripts, vol. 18.Ottawa: Institute of Mediaeval Music, [1991].

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———, ed. Johannis Tinctoris: Opera Theoretica. 2 vols. Corpus Scriptorum deMusica, vol. 22. S.l.: American Institute of Musicology, 1975–78 (1975, vol. 22/1;1978, vol. 22/2). (See Tinctoris.)

———, trans. Johannes Tinctoris (1446?–1511): Concerning the Nature and Propriety ofTones (De natura et proprietate tonorum). Translations, vol. 2. Colorado Springs:Colorado College Music Press, 1976. (See Tinctoris 1476.)

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———, trans. Bonaventura da Brescia: Rules of Plain Music (Breviloquium Musicale).Colorado Springs: Colorado College Music Press, 1979a. (See da Brescia 1497.)

———, ed. and trans. Stephano Vanneo (1493–15--): Recanetum de musica aurea, LiberII, Capituli XX–XXXVII [De proportione]. Texts and Translations, vol. 2.Colorado Springs: Colorado College Music Press, 1979b. (See Vanneo 1533.)

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———, ed. Guido Aretini: Micrologus. Corpus Scriptorum de Musica, vol. 4. S.l.:American Institute of Musicology, 1955. (See Guido d'Arezzo ca. 1026–28.)

———, ed. Expositiones in Micrologum Guidonis Aretini. Musicologica Medii Aevi, vol.1. Amsterdam : North-Holland, 1957. (See Anon. Comment. Microl. 1070/1100.)

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St Emmeram Anonymous. (See Anonymous St Emmeram.)

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———. De vera solfizationis quam vocant docendae ratione ad Magistrum FranciscumSalinam Dominum suum . p. 1570. Source: E-Mbn, ff. 41r–45v (http://www.music.indiana.edu/tml/16th/STOVERA_MMBN6486.html).

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